{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T23:08:43Z","timestamp":1785798523416,"version":"3.56.0"},"reference-count":16,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T00:00:00Z","timestamp":1755129600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China Grant","award":["62241304"],"award-info":[{"award-number":["62241304"]}]},{"name":"the National Natural Science Foundation of China Grant","award":["2018JJB170055"],"award-info":[{"award-number":["2018JJB170055"]}]},{"name":"the National Natural Science Foundation of China Grant","award":["2025GXNSFAA069293"],"award-info":[{"award-number":["2025GXNSFAA069293"]}]},{"name":"the National Natural Science Foundation of China Grant","award":["TS2024111"],"award-info":[{"award-number":["TS2024111"]}]},{"name":"the Natural Science Foundation of Guangxi Grant","award":["62241304"],"award-info":[{"award-number":["62241304"]}]},{"name":"the Natural Science Foundation of Guangxi Grant","award":["2018JJB170055"],"award-info":[{"award-number":["2018JJB170055"]}]},{"name":"the Natural Science Foundation of Guangxi Grant","award":["2025GXNSFAA069293"],"award-info":[{"award-number":["2025GXNSFAA069293"]}]},{"name":"the Natural Science Foundation of Guangxi Grant","award":["TS2024111"],"award-info":[{"award-number":["TS2024111"]}]},{"name":"Research on dynamic mechanism and fault identification method of key friction pairs of aerospace high-speed hydraulic pumps","award":["62241304"],"award-info":[{"award-number":["62241304"]}]},{"name":"Research on dynamic mechanism and fault identification method of key friction pairs of aerospace high-speed hydraulic pumps","award":["2018JJB170055"],"award-info":[{"award-number":["2018JJB170055"]}]},{"name":"Research on dynamic mechanism and fault identification method of key friction pairs of aerospace high-speed hydraulic pumps","award":["2025GXNSFAA069293"],"award-info":[{"award-number":["2025GXNSFAA069293"]}]},{"name":"Research on dynamic mechanism and fault identification method of key friction pairs of aerospace high-speed hydraulic pumps","award":["TS2024111"],"award-info":[{"award-number":["TS2024111"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To address the issue of low trajectory tracking accuracy in six-degree-of-freedom robotic arms, this study proposes a trajectory tracking control strategy that integrates a Radial Basis Function Neural Network (RBFNN) with non-singular fast terminal sliding mode (NFTSM) control. (1) The Lagrangian method is utilized to develop the dynamic model of the robotic arm. At the same time, a non-singular fast terminal sliding surface is designed to accelerate trajectory convergence and resolve the singularity problem commonly associated with traditional sliding mode control by integrating nonlinear and fast terminal terms. (2) The RBF neural network is employed to globally approximate and compensate for uncertainties in the model and variations in the parameters of the robotic arm. (3) To confirm the overall stability of the control system with the proposed NFTSM control strategy, the Lyapunov stability theory is applied to formulate a Lyapunov function. (4) The six-degree-of-freedom robotic manipulator is simulated in the MATLAB\/Simulink environment to assess the effectiveness of the proposed control method. In addition, experimental validation is carried out on a real robotic manipulator to verify the effectiveness of the proposed method. The simulation and experimental results show that, compared with NFTSM and RBFNN-SMC, the proposed control strategy significantly enhances the trajectory tracking accuracy of the six-degree-of-freedom robotic manipulator, thereby offering an effective and practical solution for its trajectory tracking control.<\/jats:p>","DOI":"10.3390\/sym17081319","type":"journal-article","created":{"date-parts":[[2025,8,14]],"date-time":"2025-08-14T14:51:46Z","timestamp":1755183106000},"page":"1319","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Trajectory Tracking Closed-Loop Cooperative Control of Manipulator Neural Network and Terminal Sliding Model"],"prefix":"10.3390","volume":"17","author":[{"given":"Deqing","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhonggang","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Guangxi Key Laboratory of Special Engineering Equipment and Control, Guilin University of Aerospace Technology, Guilin 541004, China"},{"name":"Key Laboratory of Special Engineering Equipment Design and Intelligent Drive Technology, Guilin University of Aerospace Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhong","family":"Liu","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Special Engineering Equipment and Control, Guilin University of Aerospace Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengyi","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mechanical and Control Engineering, Guilin University of Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shunjie","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mechanical and Control Engineering, Guilin University of Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiabao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xintao","family":"Liu","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory of Special Engineering Equipment and Control, Guilin University of Aerospace Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingyu","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"181","DOI":"10.3901\/JME.2022.18.181","article-title":"Trajectory tracking method of human-robot cooperative robot based on sliding mode and fuzzy algorithm","volume":"58","author":"Tao","year":"2022","journal-title":"J. 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Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1319\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:27:05Z","timestamp":1760034425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1319"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,14]]},"references-count":16,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081319"],"URL":"https:\/\/doi.org\/10.3390\/sym17081319","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,14]]}}}