{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T21:51:27Z","timestamp":1774475487204,"version":"3.50.1"},"reference-count":60,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62173352"],"award-info":[{"award-number":["62173352"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:p>Recent years have witnessed the remarkable advancements in Koopman-operator-based data-driven methods for continuum robot control. However, there is currently a paucity of both theoretical and practical work investigating the convergence and robustness of these methods, which is crucial due to the complexity and susceptibility of continuum robots and the training-to-reality gap. This work seeks to complete Koopman-operator-based methods in terms of accuracy, robustness, generalizability, and theoretical analysis while maintaining high computational efficiency. In this work, we learn the continuous-time model of continuum robots using a deep Koopman network, which bridges the gap between unknown robot models and model-dependent iterative learning control, and propose a novel control framework for data-driven control of continuum robots. Rigorous theoretical analysis is then provided to prove the convergence and robustness of the proposed method. Finally, comprehensive comparisons of three types of Koopman-operator-based methods are conducted, using six metrics to evaluate their performance. Experiments on two heterogeneous continuum robots indicate that our proposed method outperforms existing Koopman-operator-based control methods across most metrics, significantly improving robustness and generalizability. Furthermore, this work has guiding significance for applying Koopman-operator-based control methods to the efficient and robust control of other robotic systems.<\/jats:p>","DOI":"10.1177\/02783649251351046","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T08:59:50Z","timestamp":1750841990000},"page":"308-327","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["On the learning-based control of continuum robots with provable robustness, efficiency, and generalizability"],"prefix":"10.1177","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6310-514X","authenticated-orcid":false,"given":"Peng","family":"Yu","sequence":"first","affiliation":[{"name":"Sun Yat-sen University"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0710-6409","authenticated-orcid":false,"given":"Ning","family":"Tan","sequence":"additional","affiliation":[{"name":"Sun Yat-sen University"}]}],"member":"179","published-online":{"date-parts":[[2025,6,25]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2006.1636313"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2019.XV.060"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2020.3038693"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.1126\/scirobotics.adf9001"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2015.2489500"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2023.3349052"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/TASE.2024.3377291"},{"key":"e_1_3_4_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/CDC45484.2021.9683673"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/MRA.2016.2636360"},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/IROS40897.2019.8967668"},{"key":"e_1_3_4_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2020.2967269"},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364919897292"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCS.2023.3253419"},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmapro.2019.01.024"},{"key":"e_1_3_4_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2021.3138222"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2024.3360950"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2018.2861900"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1126\/scirobotics.add6864"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.1038\/s42256-023-00622-8"},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA48891.2023.10161275"},{"key":"e_1_3_4_22_1","first-page":"1","volume-title":"International Conference on Mechatronics-Mechatronika","author":"Kolpashchikov DY","year":"2018","unstructured":"Kolpashchikov DY, Laptev NV, Danilov VV, et al. 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