{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T06:12:32Z","timestamp":1779257552248,"version":"3.51.4"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SIViP"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1007\/s11760-026-05379-2","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T05:41:45Z","timestamp":1779255705000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A hybrid hierarchical dual-layer kernelized movement primitive framework for accurate and smooth robot trajectory adaptation"],"prefix":"10.1007","volume":"20","author":[{"given":"Zhe","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Zou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jilong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,20]]},"reference":[{"key":"5379_CR1","doi-asserted-by":"crossref","unstructured":"Yang, C., Lu, Z., Wang, N.: Hybrid Learning and Control Using Improved Dynamical Movement Primitive and Adaptive Neural Network Control, pp. 97\u2013123. Springer, Cham (2025)","DOI":"10.1007\/978-3-031-78501-6_5"},{"key":"5379_CR2","unstructured":"Ijspeert, A.J., Nakanishi, J., Schaal, S.: Learning attractor landscapes for learning motor primitives (2002)"},{"key":"5379_CR3","doi-asserted-by":"crossref","unstructured":"Dou, S., Xiao, J., Zhao, W., Yuan, H., Liu, H.: A robot skill learning framework based on compliant movement primitives. Journal of Intelligent and Robotic Systems 104 (2022)","DOI":"10.1007\/s10846-022-01605-4"},{"key":"5379_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.aei.2024.102625","volume":"62","author":"W Li","year":"2024","unstructured":"Li, W., Wang, Y., Liang, Y., Pham, D.T.: Learning from demonstration for autonomous generation of robotic trajectory: Status quo and forward-looking overview. Adv. Eng. Inform. 62, 102625 (2024)","journal-title":"Adv. Eng. Inform."},{"issue":"2","key":"5379_CR5","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1162\/NECO_a_00393","volume":"25","author":"AJ Ijspeert","year":"2013","unstructured":"Ijspeert, A.J., Nakanishi, J., Hoffmann, H., Pastor, P., Schaal, S.: Dynamical movement primitives: Learning attractor models for motor behaviors. Neural Comput. 25(2), 328\u2013373 (2013)","journal-title":"Neural Comput."},{"key":"5379_CR6","doi-asserted-by":"crossref","unstructured":"Ijspeert, A.J., Nakanishi, J., Schaal, S.: Trajectory formation for imitation with nonlinear dynamical systems. In: Proceedings 2001 IEEE\/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180), vol. 2, pp. 752\u2013757 (2001)","DOI":"10.1109\/IROS.2001.976259"},{"key":"5379_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11370-015-0187-9","volume":"9","author":"S Calinon","year":"2016","unstructured":"Calinon, S.: A tutorial on task-parameterized movement learning and retrieval. Intel. Serv. Robot. 9, 1\u201329 (2016)","journal-title":"Intel. Serv. Robot."},{"key":"5379_CR8","unstructured":"Paraschos, A., Daniel, C., Peters, J., Neumann, G.: Probabilistic movement primitives. In: Proceedings of the 27th International Conference on Neural Information Processing Systems - Volume 2. NIPS\u201913, pp. 2616\u20132624. Curran Associates Inc., Red Hook, NY, USA (2013)"},{"key":"5379_CR9","doi-asserted-by":"crossref","unstructured":"Gomez-Gonzalez, S., Neumann, G., Sch\u00f6lkopf, B., Peters, J.: Using probabilistic movement primitives for striking movements. In: 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pp. 502\u2013508 (2016)","DOI":"10.1109\/HUMANOIDS.2016.7803322"},{"key":"5379_CR10","doi-asserted-by":"crossref","unstructured":"Huang, Y., Rozo, L., Silv\u00e9rio, J.a., Caldwell, D.G.: Kernelized movement primitives. Int. J. Rob. Res. 38(7), 833\u2013852 (2019)","DOI":"10.1177\/0278364919846363"},{"key":"5379_CR11","doi-asserted-by":"crossref","unstructured":"Huang, Y., Rozo, L., Silv\u00e9rio, J., Caldwell, D.G.: Non-parametric imitation learning of robot motor skills. In: 2019 International Conference on Robotics and Automation (ICRA), pp. 5266\u20135272 (2019)","DOI":"10.1109\/ICRA.2019.8794267"},{"key":"5379_CR12","doi-asserted-by":"crossref","unstructured":"Silv\u00e9rio, J., Huang, Y., Abu-Dakka, F.J., Rozo, L., Caldwell, D.G.: Uncertainty-aware imitation learning using kernelized movement primitives. In: 2019 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 90\u201397 (2019)","DOI":"10.1109\/IROS40897.2019.8967996"},{"key":"5379_CR13","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2023.111120","volume":"155","author":"Z Jin","year":"2023","unstructured":"Jin, Z., Liu, A., Zhang, W.-A., Yu, L., Yang, C.: Gaussian process movement primitive. Automatica 155, 111120 (2023)","journal-title":"Automatica"},{"issue":"11","key":"5379_CR14","first-page":"6252","volume":"32","author":"H Wen","year":"2024","unstructured":"Wen, H., Fu, W., Chen, W., Huan, J., Li, C., Duan, X.: Imitation learning and teleoperation shared control with unit tangent fuzzy movement primitives 32(11), 6252\u20136266 (2024)","journal-title":"Imitation learning and teleoperation shared control with unit tangent fuzzy movement primitives"},{"key":"5379_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.rcim.2025.102983","volume":"94","author":"T Xu","year":"2025","unstructured":"Xu, T., Singh, S., Chang, Q.: Generalizing kinematic skill learning to energy efficient dynamic motion planning using optimized dynamic movement primitives. Robotics and Computer-Integrated Manufacturing 94, 102983 (2025)","journal-title":"Robotics and Computer-Integrated Manufacturing"},{"key":"5379_CR16","doi-asserted-by":"crossref","unstructured":"Liu, Z., Fang, Y.: A novel dmps framework for robot skill generalizing with obstacle avoidance: Taking volume and orientation into consideration. IEEE\/ASME Transactions on Mechatronics, 1\u201311 (2025)","DOI":"10.1109\/TMECH.2024.3524207"},{"key":"5379_CR17","doi-asserted-by":"crossref","unstructured":"Sidiropoulos, A., Doulgeri, Z.: Dynamic via-points and improved spatial generalization for online trajectory generation with dynamic movement primitives. J. Intell. Robotics Syst. 110(1), 18 (2024)","DOI":"10.1007\/s10846-024-02051-0"},{"key":"5379_CR18","doi-asserted-by":"crossref","unstructured":"Kober, J., M\u00fclling, K., Kr\u00f6mer, O., Lampert, C.H., Sch\u00f6lkopf, B., Peters, J.: Movement templates for learning of hitting and batting. In: 2010 IEEE International Conference on Robotics and Automation, pp. 853\u2013858 (2010)","DOI":"10.1109\/ROBOT.2010.5509672"},{"key":"5379_CR19","doi-asserted-by":"publisher","first-page":"2868","DOI":"10.1109\/TRO.2024.3390052","volume":"40","author":"S Ruan","year":"2024","unstructured":"Ruan, S., Liu, W., Wang, X., Meng, X., Chirikjian, G.S.: Primp: Probabilistically-informed motion primitives for efficient affordance learning from demonstration. IEEE Trans. Rob. 40, 2868\u20132887 (2024)","journal-title":"IEEE Trans. Rob."},{"key":"5379_CR20","doi-asserted-by":"crossref","unstructured":"Hershey, J.R., Olsen, P.A.: Approximating the kullback leibler divergence between gaussian mixture models. In: 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP \u201907, vol. 4, pp. 317\u2013320 (2007)","DOI":"10.1109\/ICASSP.2007.366913"},{"key":"5379_CR21","doi-asserted-by":"publisher","first-page":"522","DOI":"10.1016\/j.neucom.2021.08.036","volume":"464","author":"H Wu","year":"2021","unstructured":"Wu, H., Yan, W., Xu, Z., Li, S., Zhou, X.: Learning robot anomaly recovery skills from multiple time-driven demonstrations. Neurocomputing 464, 522\u2013532 (2021)","journal-title":"Neurocomputing"},{"key":"5379_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2024.127711","volume":"589","author":"J Fu","year":"2024","unstructured":"Fu, J., Jin, Z., Liu, A., Zhang, W.-A., Yu, L.: Non-parametric gaussian process movement primitive with via-point constraint for effective and safe robot skill learning. Neurocomputing 589, 127711 (2024)","journal-title":"Neurocomputing"},{"key":"5379_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2023.126781","volume":"558","author":"K Hu","year":"2023","unstructured":"Hu, K., Zhang, J., Wu, D.: Kernelized gradient descent method for learning from demonstration. Neurocomputing 558, 126781 (2023)","journal-title":"Neurocomputing"},{"issue":"1","key":"5379_CR24","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1109\/TIE.2024.3384602","volume":"72","author":"H Wu","year":"2025","unstructured":"Wu, H., Zhai, D.-H., Xia, Y.: Probabilized dynamic movement primitives and model predictive planning for enhanced trajectory imitation learning. IEEE Trans. Industr. Electron. 72(1), 620\u2013628 (2025)","journal-title":"IEEE Trans. Industr. Electron."},{"key":"5379_CR25","doi-asserted-by":"crossref","unstructured":"Calinon, S., Guenter, F., Billard, A.: On learning, representing, and generalizing a task in a humanoid robot. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 37(2), 286\u2013298 (2007)","DOI":"10.1109\/TSMCB.2006.886952"},{"key":"5379_CR26","doi-asserted-by":"crossref","unstructured":"Bringmann, K., Fischer, N., Hoog, I., Kipouridis, E., Kociumaka, T., Rotenberg, E.: Dynamic Dynamic Time Warping (2023)","DOI":"10.1137\/1.9781611977912.10"},{"issue":"2","key":"5379_CR27","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1002\/wics.199","volume":"4","author":"AA Neath","year":"2012","unstructured":"Neath, A.A., Cavanaugh, J.E.: The bayesian information criterion: background, derivation, and applications. WIREs Comput. Stat. 4(2), 199\u2013203 (2012)","journal-title":"WIREs Comput. Stat."},{"issue":"11","key":"5379_CR28","doi-asserted-by":"publisher","first-page":"3338","DOI":"10.1109\/TNNLS.2019.2891088","volume":"30","author":"D Chang","year":"2019","unstructured":"Chang, D., Sun, S., Zhang, C.: An accelerated linearly convergent stochastic l-bfgs algorithm. IEEE Transactions on Neural Networks and Learning Systems 30(11), 3338\u20133346 (2019)","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"5379_CR29","doi-asserted-by":"crossref","unstructured":"Qi, P., Zhou, W., Han, J.: A method for stochastic l-bfgs optimization. In: 2017 IEEE 2nd International Conference on Cloud Computing and Big Data Analysis (ICCCBDA), pp. 156\u2013160 (2017)","DOI":"10.1109\/ICCCBDA.2017.7951902"},{"key":"5379_CR30","doi-asserted-by":"crossref","unstructured":"Prados, A., Espinoza, G., Moreno, L., Barber, R.: Segment, compare, and learn: Creating movement libraries of complex task for learning from demonstration. Biomimetics 10(1) (2025)","DOI":"10.3390\/biomimetics10010064"},{"key":"5379_CR31","doi-asserted-by":"crossref","unstructured":"Calinon, S., Lee, D.: In: Goswami, A., Vadakkepat, P. (eds.) Learning Control, pp. 1261\u20131312. Springer, Dordrecht (2019)","DOI":"10.1007\/978-94-007-6046-2_68"},{"issue":"1","key":"5379_CR32","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1109\/TIE.2023.3250746","volume":"71","author":"A Liu","year":"2024","unstructured":"Liu, A., Zhan, S., Jin, Z., Zhang, W.-A.: A variable impedance skill learning algorithm based on kernelized movement primitives. IEEE Trans. Industr. Electron. 71(1), 870\u2013879 (2024)","journal-title":"IEEE Trans. Industr. Electron."}],"container-title":["Signal, Image and Video Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-026-05379-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11760-026-05379-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-026-05379-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T05:41:51Z","timestamp":1779255711000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11760-026-05379-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["5379"],"URL":"https:\/\/doi.org\/10.1007\/s11760-026-05379-2","relation":{},"ISSN":["1863-1703","1863-1711"],"issn-type":[{"value":"1863-1703","type":"print"},{"value":"1863-1711","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"20 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 April 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 May 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}],"article-number":"343"}}