{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T15:04:20Z","timestamp":1773759860096,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T00:00:00Z","timestamp":1646352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2019YFB1312404"],"award-info":[{"award-number":["2019YFB1312404"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51975401"],"award-info":[{"award-number":["51975401"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51875393"],"award-info":[{"award-number":["51875393"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Supported by State Key Laboratory of Robotics and System (HIT)","award":["20210315"],"award-info":[{"award-number":["20210315"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>A nonlinear stiffness actuator (NSA) can achieve high torque\/force resolution in the low stiffness range and high bandwidth in the high stiffness range. However, for the NSA, due to the imperfect performance of the elastic mechanical component such as friction, hysteresis, and unmeasurable energy consumption caused by former factors, it is more difficult to achieve accurate position control compared to the rigid actuator. Moreover, for a compliant robot with multiple degree of freedoms (DOFs) driven by NSAs, the influence of every NSA on the trajectory of the end effector is different and even coupled. Therefore, it is a challenge to implement precise trajectory control on a robot driven by such NSAs. In this paper, a control algorithm based on the Terminal Sliding Mode (TSM) approach is proposed to control the end effector trajectory of the compliant robot with multiple DOFs driven by NSAs. This control algorithm reduces the coupling of the driving torque, and mitigates the influence of parametric variation. The closed-loop system\u2019s finite time convergence and stability are mathematically established via the Lyapunov stability theory. Moreover, under the same experimental conditions, by the comparison between the Proportion Differentiation (PD) controller and the controller using TSM method, the algorithm\u2019s efficacy is experimentally verified on the developed compliant robot. The results show that the trajectory tracking is more accurate for the controller using the TSM method compared to the PD controller.<\/jats:p>","DOI":"10.3390\/mi13030409","type":"journal-article","created":{"date-parts":[[2022,3,6]],"date-time":"2022-03-06T20:40:02Z","timestamp":1646599202000},"page":"409","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Trajectory Tracking Control Based on a Terminal Sliding Mode for a Compliant Robot with Nonlinear Stiffness Joints"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3715-2003","authenticated-orcid":false,"given":"Zhibin","family":"Song","sequence":"first","affiliation":[{"name":"Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China"},{"name":"School of Mechanical Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianyu","family":"Ma","sequence":"additional","affiliation":[{"name":"Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China"},{"name":"School of Mechanical Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keke","family":"Qi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China"},{"name":"School of Mechanical Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7448-8529","authenticated-orcid":false,"given":"Emmanouil","family":"Spyrakos-Papastavridis","sequence":"additional","affiliation":[{"name":"Centre for Robotics Research, Department of Engineering, King\u2019s College, London WC2R 2LS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9837-098X","authenticated-orcid":false,"given":"Songyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rongjie","family":"Kang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China"},{"name":"School of Mechanical Engineering, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/TMECH.2015.2465849","article-title":"A Review of Algorithms for Compliant Control of Stiff and Fixed-Compliance Robots","volume":"21","author":"Calanca","year":"2015","journal-title":"IEEE\/ASME Trans. 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