{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T06:24:54Z","timestamp":1766298294988,"version":"3.41.2"},"reference-count":45,"publisher":"Emerald","issue":"2","license":[{"start":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T00:00:00Z","timestamp":1731542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IR"],"published-print":{"date-parts":[[2025,3,4]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>Assisted training using upper limb rehabilitation robots is beneficial for flaccid paralysis patients in recovering their functional abilities. In the assisted training mode, the patient\u2019s motor ability is limited by factors such as limb muscle tension, and it is prone for the rehabilitation robot to deviate from the prescribed training trajectory. A sliding mode control method based on a fixed time observer is proposed to address the problem of delayed trajectory tracking response of upper limb rehabilitation robots caused by external disturbances such as patient limbs.<\/jats:p>\n<\/jats:sec>\n<jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>First, aiming at the problem of estimating and compensating for external disturbances in the upper limb rehabilitation robot system, a fixed time observer was designed based on the robot\u2019s dynamic model. Second, the composite sliding mode reaching law combining the smooth function and the power-exponential function is proposed to shorten the convergence time of system states in the startup phase, thereby reducing chattering in the control process and realizing the real-time tracking of the training trajectory by the control system.<\/jats:p>\n<\/jats:sec>\n<jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>The proposed method provides a solution for the trajectory tracking speed of upper limb rehabilitation robot controllers. In the circular trajectory tracking control, compared to the sliding-mode control method combined with the variable-exponential composite reaching law based on the fixed-time observer, the method in this paper reduces the time for the system state to reach the sliding surface by 0.89\u2009s and improves the response speed by 0.66%.<\/jats:p>\n<\/jats:sec>\n<jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>The composite sliding mode approach law based on smooth function and power exponent function can reduce the time it takes for the system state to reach and remain on the sliding surface and improve the trajectory tracking speed of upper limb rehabilitation robots. This controller improves the accuracy of trajectory control and ensures the robustness of auxiliary rehabilitation training.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/ir-06-2024-0248","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T04:45:13Z","timestamp":1731386713000},"page":"277-286","source":"Crossref","is-referenced-by-count":2,"title":["The sliding mode controller with composite reaching law for upper limb rehabilitation robot"],"prefix":"10.1108","volume":"52","author":[{"given":"Peng","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luyu","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fanghao","family":"Nan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RenQuan","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"issue":"1","key":"key2025022811245808300_ref001","first-page":"129","article-title":"Analytical model of hand phalanges desired trajectory for rehabilitation and design a sliding mode controller based on this model","volume":"20","year":"2020","journal-title":"Modares Mechanical Engineering"},{"issue":"2","key":"key2025022811245808300_ref002","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1177\/2516608519864760","article-title":"Task-oriented motor learning in upper extremity rehabilitation post stroke","volume":"2","year":"2019","journal-title":"Journal of Stroke Medicine"},{"first-page":"331","article-title":"Developing a VR training environment for fingers rehabilitation","year":"2022","key":"key2025022811245808300_ref003"},{"issue":"7\/8","key":"key2025022811245808300_ref004","first-page":"10775463231165094","article-title":"Fixed time sliding mode control for disturbed robotic manipulator","volume":"30","year":"2023","journal-title":"Journal of Vibration and Control"},{"first-page":"694","article-title":"Sliding mode control of an exoskeleton robot for use in upper limb rehabilitation","year":"2015","key":"key2025022811245808300_ref005"},{"issue":"10","key":"key2025022811245808300_ref006","first-page":"1845","article-title":"Flatness tracking control scheme of rehabilitation exoskeleton robot with dynamic uncertainties","volume":"236","year":"2022","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"},{"issue":"7","key":"key2025022811245808300_ref007","first-page":"2518","article-title":"A novel variable exponential discrete time sliding mode reaching law","volume":"68","year":"2021","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"issue":"2","key":"key2025022811245808300_ref008","first-page":"600","article-title":"Sliding-mode robot control with exponential reaching law","volume":"58","year":"2010","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"4","key":"key2025022811245808300_ref009","first-page":"513","article-title":"Active vibration control of electric drive system in electric vehicles based on active disturbance rejection current compensation under impact conditions","volume":"7","year":"2023","journal-title":"SAE International Journal of Vehicle Dynamics, Stability, and NVH"},{"issue":"3","key":"key2025022811245808300_ref010","first-page":"233","article-title":"Robot-assisted post-stroke motion rehabilitation in upper extremities: a survey","volume":"16","year":"2017","journal-title":"International Journal on Disability and Human Development"},{"key":"key2025022811245808300_ref011","first-page":"1406","article-title":"Effects of task oriented rehabilitation of upper extremity after stroke: a systematic review","volume":"72","year":"2022","journal-title":"Journal of the Pakistan Medical Association"},{"issue":"11","key":"key2025022811245808300_ref012","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.3390\/math10111935","article-title":"Sliding mode control of manipulator based on improved reaching law and sliding surface","volume":"10","year":"2022","journal-title":"Mathematics"},{"issue":"11","key":"key2025022811245808300_ref013","doi-asserted-by":"crossref","first-page":"12110","DOI":"10.1109\/TPEL.2020.2986893","article-title":"Adaptive speed control of PMSM drive system based a new sliding-mode reaching law","volume":"35","year":"2020","journal-title":"IEEE Transactions on Power Electronics"},{"issue":"6","key":"key2025022811245808300_ref014","doi-asserted-by":"crossref","first-page":"2636","DOI":"10.1007\/s12555-016-0736-9","article-title":"Power rate exponential reaching law for enhanced performance of sliding mode control","volume":"15","year":"2017","journal-title":"International Journal of Control, Automation and Systems"},{"key":"key2025022811245808300_ref015","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1109\/MMAR.2017.8046882","article-title":"Sliding mode control based on the reaching law approach\u2014a brief survey","volume-title":"2017 22nd International conference on methods and models in automation and robotics (MMAR)","year":"2017"},{"key":"key2025022811245808300_ref016","doi-asserted-by":"crossref","first-page":"43284","DOI":"10.1109\/ACCESS.2022.3165091","article-title":"Finite-time fault-tolerant control for a Stewart platform using sliding mode control with improved reaching law","volume":"10","year":"2022","journal-title":"IEEE Access"},{"key":"key2025022811245808300_ref017","doi-asserted-by":"crossref","first-page":"106774","DOI":"10.1016\/j.ymssp.2020.106774","article-title":"An observer-based fixed-time position tracking strategy for DC torque motor systems","volume":"142","year":"2020","journal-title":"Mechanical Systems and Signal Processing"},{"issue":"3","key":"key2025022811245808300_ref018","first-page":"498","article-title":"Sliding mode control with double power reaching law","volume":"31","year":"2016","journal-title":"Control and Decision"},{"issue":"7\/8","key":"key2025022811245808300_ref019","first-page":"1142","article-title":"Trajectory tracking control of upper limb rehabilitation robot based on optimal discrete sliding mode control","volume":"56","year":"2023","journal-title":"Measurement and Control"},{"issue":"4","key":"key2025022811245808300_ref020","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.1007\/s11071-018-4324-9","article-title":"Chattering reduced sliding mode control for a class of chaotic systems","volume":"93","year":"2018","journal-title":"Nonlinear Dynamics"},{"key":"key2025022811245808300_ref021","first-page":"1","article-title":"Weakened effective connectivity related to electroacupuncture in stroke patients with prolonged flaccid paralysis: an EEG pilot study","volume":"2021","year":"2021","journal-title":"Neural Plasticity"},{"issue":"6","key":"key2025022811245808300_ref022","first-page":"4629","article-title":"Discrete-time sliding-mode control with enhanced power reaching law","volume":"66","year":"2018","journal-title":"IEEE Transactions on Industrial Electronics"},{"key":"key2025022811245808300_ref023","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1016\/j.automatica.2017.04.009","article-title":"Fixed-time observer with simple gains for uncertain systems","volume":"81","year":"2017","journal-title":"Automatica"},{"issue":"10","key":"key2025022811245808300_ref024","doi-asserted-by":"crossref","first-page":"6148","DOI":"10.1109\/TIE.2016.2570718","article-title":"Sliding mode control of PMSG wind turbine based on enhanced exponential reaching law","volume":"63","year":"2016","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"12","key":"key2025022811245808300_ref025","first-page":"7838","article-title":"Global finite time active disturbance rejection control for parallel manipulators with unknown bounded uncertainties","volume":"51","year":"2020","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"issue":"4","key":"key2025022811245808300_ref026","first-page":"2841","article-title":"Exponential reaching law sliding mode control for dual arm robots","volume":"15","year":"2020","journal-title":"Journal of Engineering Science and Technology"},{"issue":"4","key":"key2025022811245808300_ref027","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1109\/TMRB.2020.3034497","article-title":"A multi-functional lower-and upper limb stroke rehabilitation robot","volume":"2","year":"2020","journal-title":"IEEE Transactions on Medical Robotics and Bionics"},{"issue":"6","key":"key2025022811245808300_ref028","doi-asserted-by":"crossref","first-page":"2878","DOI":"10.1007\/s12555-017-0616-y","article-title":"Control algorithms of magnetic suspension systems based on the improved double exponential reaching law of sliding mode control","volume":"16","year":"2018","journal-title":"International Journal of Control, Automation and Systems"},{"issue":"12","key":"key2025022811245808300_ref029","doi-asserted-by":"crossref","first-page":"8066","DOI":"10.1109\/TII.2021.3059774","article-title":"Fixed-time-convergent generalized extended state observer based motor control subject to multiple disturbances","volume":"17","year":"2021","journal-title":"IEEE Transactions on Industrial Informatics"},{"issue":"1","key":"key2025022811245808300_ref030","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1007\/s12555-011-0135-1","article-title":"Control of an exoskeleton robot arm with sliding mode exponential reaching law","volume":"11","year":"2013","journal-title":"International Journal of Control, Automation and Systems"},{"issue":"4","key":"key2025022811245808300_ref031","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1002\/rnc.5346","article-title":"A new approach to design a finite\u2010time extended state observer: uncertain robotic manipulators application","volume":"31","year":"2021","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"1","key":"key2025022811245808300_ref032","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1016\/j.jfranklin.2020.11.018","article-title":"Fractional power rate reaching law for augmented sliding mode performance","volume":"358","year":"2021","journal-title":"Journal of the Franklin Institute"},{"issue":"4","key":"key2025022811245808300_ref033","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1080\/10749357.2022.2035578","article-title":"A systematic review of randomized controlled trial characteristics for interventions to improve upper extremity motor recovery post stroke","volume":"30","year":"2023","journal-title":"Topics in Stroke Rehabilitation"},{"issue":"6","key":"key2025022811245808300_ref034","doi-asserted-by":"crossref","first-page":"64502","DOI":"10.1115\/1.4042743","article-title":"Fixed-time inverse dynamics control for robot manipulators","volume":"141","year":"2019","journal-title":"Journal of Dynamic Systems, Measurement, and Control"},{"issue":"9","key":"key2025022811245808300_ref035","article-title":"Adaptive fuzzy fault tolerant control for robot manipulators with fixed-time convergence","volume":"31","year":"2023","journal-title":"IEEE Transactions on Fuzzy Systems"},{"issue":"1","key":"key2025022811245808300_ref036","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1108\/IR-07-2023-0146","article-title":"Research on fuzzy impedance control of upper limb rehabilitation robot based on membership functions online optimization learning strategy","volume":"51","year":"2024","journal-title":"Industrial Robot: The International Journal of Robotics Research and Application"},{"key":"key2025022811245808300_ref037","first-page":"40","article-title":"Composite finite-time control for a high order nonlinear uncertain system","year":"2023","journal-title":"Control Theory & Applications"},{"issue":"4","key":"key2025022811245808300_ref038","first-page":"4117","article-title":"A new reaching law for antidisturbance sliding-mode control of PMSM speed regulation system","volume":"35","year":"2019","journal-title":"IEEE Transactions on Power Electronics"},{"issue":"2","key":"key2025022811245808300_ref039","first-page":"257","article-title":"Observer-based finite-time control for trajectory tracking of lower extremity exoskeleton","volume":"236","year":"2022","journal-title":"Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"},{"issue":"3","key":"key2025022811245808300_ref040","doi-asserted-by":"crossref","first-page":"1729881419847899","DOI":"10.1177\/1729881419847899","article-title":"Research on trajectory tracking control of manipulator based on modified terminal sliding mode with double power reaching law","volume":"16","year":"2019","journal-title":"International Journal of Advanced Robotic Systems"},{"issue":"5","key":"key2025022811245808300_ref041","first-page":"714","article-title":"Design of fixed time observer and adaptive synovial control method for manipulator","volume":"39","year":"2020","journal-title":"Mechanical Science and Technology for Aerospace Engineering"},{"issue":"5","key":"key2025022811245808300_ref042","first-page":"917","article-title":"Fixed-time convergent disturbance observer for first-order uncertain system","volume":"34","year":"2019","journal-title":"Control and Decision"},{"issue":"16","key":"key2025022811245808300_ref043","doi-asserted-by":"crossref","first-page":"1865","DOI":"10.1002\/rnc.1666","article-title":"Nonsingular fast terminal sliding\u2010mode control for nonlinear dynamical systems","volume":"21","year":"2011","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"9","key":"key2025022811245808300_ref044","doi-asserted-by":"crossref","first-page":"258","DOI":"10.3390\/act11090258","article-title":"Fast terminal sliding mode control based on finite-time observer and improved reaching law for aerial robots","volume":"11","year":"2022","journal-title":"Actuators"},{"issue":"2","key":"key2025022811245808300_ref045","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1080\/00207721.2017.1406553","article-title":"Finite-time containment control of perturbed multi-agent systems based on sliding-mode control","volume":"49","year":"2018","journal-title":"International Journal of Systems Science"}],"container-title":["Industrial Robot: the international journal of robotics research and application"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IR-06-2024-0248\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/IR-06-2024-0248\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:39:24Z","timestamp":1753393164000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/ir\/article\/52\/2\/277-286\/1239443"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,14]]},"references-count":45,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,11,14]]},"published-print":{"date-parts":[[2025,3,4]]}},"alternative-id":["10.1108\/IR-06-2024-0248"],"URL":"https:\/\/doi.org\/10.1108\/ir-06-2024-0248","relation":{},"ISSN":["0143-991X","1758-5791"],"issn-type":[{"type":"print","value":"0143-991X"},{"type":"electronic","value":"1758-5791"}],"subject":[],"published":{"date-parts":[[2024,11,14]]}}}