{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T09:06:42Z","timestamp":1773047202062,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51922093"],"award-info":[{"award-number":["51922093"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51975506"],"award-info":[{"award-number":["51975506"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["51905465"],"award-info":[{"award-number":["51905465"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"published-print":{"date-parts":[[2023,5]]},"DOI":"10.1007\/s10846-023-01845-y","type":"journal-article","created":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T15:01:41Z","timestamp":1683212501000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["High\u2011accuracy Impedance Compound Control of the Actuator for Periodic Gait of Legged Robots"],"prefix":"10.1007","volume":"108","author":[{"given":"Qixin","family":"Zhu","sequence":"first","affiliation":[]},{"given":"Bin","family":"Yu","sequence":"additional","affiliation":[]},{"given":"Xinjie","family":"Li","sequence":"additional","affiliation":[]},{"given":"Junhui","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Huaizhi","family":"Zong","sequence":"additional","affiliation":[]},{"given":"Kaixian","family":"Ba","sequence":"additional","affiliation":[]},{"given":"Xiangdong","family":"Kong","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,5,4]]},"reference":[{"issue":"1","key":"1845_CR1","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1109\/LRA.2020.3039730","volume":"6","author":"R Sonker","year":"2021","unstructured":"Sonker, R., Dutta, A.: Adding terrain height to improve model learning for path tracking on uneven terrain by a four wheel robot. IEEE Robot. Autom. Lett. 6(1), 239\u2013246 (2021). https:\/\/doi.org\/10.1109\/LRA.2020.3039730","journal-title":"IEEE Robot. Autom. Lett."},{"issue":"9","key":"1845_CR2","doi-asserted-by":"publisher","first-page":"3757","DOI":"10.3390\/app11093757","volume":"11","author":"LS Grigore","year":"2021","unstructured":"Grigore, L.S., Oncioiu, I., Priescu, I., et al.: Development and evaluation of the traction characteristics of a crawler EOD robot. Appl. Sci. Basel 11(9), 3757 (2021)","journal-title":"Appl. Sci. Basel"},{"key":"1845_CR3","doi-asserted-by":"publisher","unstructured":"Ba, K.X., Song, Y.h., Wang, C.Y., et al.: A novel kinematics and statics correction algorithm of semi-cylindrical foot end structure for 3-DOF LHDS of legged robots. Complex Intell. Syst.\u00a08, 5387\u20135407 (2022). https:\/\/doi.org\/10.1007\/s40747-022-00748-z","DOI":"10.1007\/s40747-022-00748-z"},{"key":"1845_CR4","doi-asserted-by":"publisher","unstructured":"Schreiber D A, Richter F, Bilan A, et al.: ARCSnake: An Archimedes\u2019 screw-propelled, reconfigurable serpentine robot for complex environments, 2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 7029\u20137034 (2020). https:\/\/doi.org\/10.1109\/ICRA40945.2020.9196968","DOI":"10.1109\/ICRA40945.2020.9196968"},{"key":"1845_CR5","doi-asserted-by":"publisher","first-page":"102499","DOI":"10.1016\/j.mechatronics.2021.102499","volume":"74","author":"ZM Cui","year":"2021","unstructured":"Cui, Z.M., Zhang, G.T., Rong, X.W., et al.: Design and motion planning of hydraulically driven leg for maximum height jumping. Mechatronics 74, 102499 (2021). https:\/\/doi.org\/10.1016\/j.mechatronics.2021.102499","journal-title":"Mechatronics"},{"key":"1845_CR6","doi-asserted-by":"crossref","unstructured":"Zhu, Q.X., Huang, D.H., Yu, Bin., et al.: An improved method combined SMC and MLESO for impedance control of legged robots\u2019 electro-hydraulic servo system.\u00a0ISA Trans.\u00a0130, 598\u2013609 (2022). https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S001905782200129X?via%3Dihub","DOI":"10.1016\/j.isatra.2022.03.009"},{"key":"1845_CR7","doi-asserted-by":"publisher","unstructured":"Playter, R., Buehler, M., Raibert, M., BigDog, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 6, pp. 239\u2013246 (2006). https:\/\/doi.org\/10.1109\/LRA.2020.3039730.","DOI":"10.1109\/LRA.2020.3039730"},{"issue":"2","key":"1845_CR8","first-page":"51","volume":"19","author":"R Scott","year":"2014","unstructured":"Scott, R., Gourley: Fully loaded: DARPA\u2019s Legged Squad Support System is able to operate over difficult terrain. Unmanned Vehicles: Dedicated to the Unmanned Systems Industry 19(2), 51\u201354 (2014)","journal-title":"Unmanned Vehicles Dedicated to the Unmanned Systems Industry"},{"key":"1845_CR9","unstructured":"Boston Dynamics. Spot [EB\/OL]. https:\/\/www.bostondynamics.com\/spot (2021) Accessed 1 June 2021"},{"issue":"3","key":"1845_CR10","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1007\/s10514-021-09974-9","volume":"45","author":"U Gabriel","year":"2021","unstructured":"Gabriel, U., Victor, B., Claudio, S., et al.: Effect of compliance on morphological control of dynamic locomotion with HyQ. Autonomous Robot 45(3), 421\u2013434 (2021). https:\/\/doi.org\/10.1007\/s10514-021-09974-9","journal-title":"Autonomous Robot"},{"issue":"2","key":"1845_CR11","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1109\/TMECH.2016.2616284","volume":"22","author":"C Semini","year":"2017","unstructured":"Semini, C., Victor, B., Jake, G., et al.: Design of the hydraulically actuated, torque-controlled quadruped robot HyQ2Max. IEEE\/ASME Trans. Mechatron. 22(2), 635\u2013646 (2017). https:\/\/doi.org\/10.1109\/TMECH.2016.2616284","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"1845_CR12","unstructured":"Semini C, Barasuol V, Focchi M, et al. Brief introduction to the quadruped robot HyQReal, Italian Conference on Robotics and Intelligent Machines, pp. 1\u20132 (2021)"},{"issue":"1","key":"1845_CR13","doi-asserted-by":"publisher","first-page":"340","DOI":"10.3390\/app10010340","volume":"10","author":"ZS Hua","year":"2020","unstructured":"Hua, Z.S., Rong, X.W., Li, Y.B., et al.: Analysis and verification on energy consumption of the quadruped robot with passive compliant hydraulic servo actuator. Appl. Sci.-Basel 10(1), 340 (2020). https:\/\/doi.org\/10.3390\/app10010340","journal-title":"Appl. Sci.-Basel"},{"key":"1845_CR14","unstructured":"Georg, W., Sylvain, B., Wu, T. F., et al.: Walking on partial footholds including line contacts with the humanoid robot atlas, International Conference on Humanoid Robots, pp. 1312\u20131319 (2016)."},{"issue":"6","key":"1845_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42235-020-0091-7","volume":"17","author":"YP Shi","year":"2020","unstructured":"Shi, Y.P., Li, M.T., Zha, F.S., et al.: Force-controlled compensation scheme for P-Q valve-controlled asymmetric cylinder used on hydraulic quadruped robots[J]. J. Bionic Eng. 17(6), 1\u201313 (2020). https:\/\/doi.org\/10.1007\/s42235-020-0091-7","journal-title":"J. Bionic Eng."},{"issue":"9","key":"1845_CR16","doi-asserted-by":"publisher","first-page":"1648","DOI":"10.3390\/rs13091648","volume":"13","author":"K Karam Dad","year":"2021","unstructured":"Karam Dad, K., Amad, Z., Muhammad Umair, A., et al.: Robust controller for pursuing trajectory and force estimations of a bilateral tele-operated hydraulic manipulator. Remote Sens. 13(9), 1648 (2021). https:\/\/doi.org\/10.3390\/rs13091648","journal-title":"Remote Sens."},{"key":"1845_CR17","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3077599","author":"D Yang","year":"2021","unstructured":"Yang, D., Zong, G.D., Su, S.F., et al.: Time-driven adaptive control of switched systems with application to electro-hydraulic unit. IEEE Trans. Cybernet. (2021). https:\/\/doi.org\/10.1109\/TCYB.2021.3077599","journal-title":"IEEE Trans. Cybernet."},{"key":"1845_CR18","doi-asserted-by":"publisher","unstructured":"Weerapong, C., Unnat, P.: Friction compensated fuzzy force tracking control of electro-hydraulic system. 2020 5th International Conference on Control and Robotics Engineering (ICCRE), pp. 114\u2013118 (2020). https:\/\/doi.org\/10.1109\/ICCRE49379.2020.9096434","DOI":"10.1109\/ICCRE49379.2020.9096434"},{"issue":"10","key":"1845_CR19","doi-asserted-by":"publisher","first-page":"1887","DOI":"10.1177\/0954406220903337","volume":"234","author":"C Cheng","year":"2020","unstructured":"Cheng, C., Liu, S.Y., Wu, H.Z.: Sliding mode observer-based fractional-order proportional\u2013integral\u2013derivative sliding mode control for electro-hydraulic servo systems. Arch. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 234(10), 1887\u20131898 (2020). https:\/\/doi.org\/10.1177\/0954406220903337","journal-title":"Arch. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci."},{"key":"1845_CR20","doi-asserted-by":"publisher","unstructured":"Hu, Y.F., Li, D.H.: An improved active disturbance rejection controller for hydraulic valve-controlled hydraulic motor. Proceedings of the 39th Chinese control conference, pp. 6037\u20136042 (2020) https:\/\/doi.org\/10.23919\/CCC50068.2020.9189405","DOI":"10.23919\/CCC50068.2020.9189405"},{"issue":"3","key":"1845_CR21","doi-asserted-by":"publisher","first-page":"172988142092461","DOI":"10.1177\/1729881420924611","volume":"17","author":"QX Zhu","year":"2020","unstructured":"Zhu, Q.X., Yu, B., Huang, Z.P., et al.: State feedback-based impedance control for legged robot hydraulic drive unit via full-dimensional state observer. Int. J. Adv. Robot. Syst. 17(3), 172988142092461 (2020). https:\/\/doi.org\/10.1177\/1729881420924611","journal-title":"Int. J. Adv. Robot. Syst."},{"issue":"8","key":"1845_CR22","doi-asserted-by":"publisher","first-page":"108090","DOI":"10.1016\/j.ymssp.2021.108090","volume":"163","author":"Q Zhang","year":"2022","unstructured":"Zhang, Q., Guo, H., Liu, Y., et al.: Robust plug-in repetitive control for speed smoothness of cascaded-PI PMSM drive. Mech. Syst. Signal Process. 163(8), 108090 (2022). https:\/\/doi.org\/10.1016\/j.ymssp.2021.108090","journal-title":"Mech. Syst. Signal Process."},{"key":"1845_CR23","doi-asserted-by":"crossref","unstructured":"Sadegh, N.: Synthesis and stability analysis of repetitive controllers. American Control Conference, pp. 2634\u20132639 (1991)","DOI":"10.23919\/ACC.1991.4791877"},{"issue":"4","key":"1845_CR24","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1109\/TCST.2002.1014674.L","volume":"10","author":"MC Tsai","year":"2002","unstructured":"Tsai, M.C., Wu, S.Y.: Design of a plug-in type repetitive controller for periodic inputs. IEEE Trans. Control Syst. Technol. 10(4), 547\u2013555 (2002). https:\/\/doi.org\/10.1109\/TCST.2002.1014674.L","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"1845_CR25","doi-asserted-by":"crossref","unstructured":"Hara, S., Yamamoto, Y.: Stability of repetitive control systems. IEEE Conference on Decision and Control, pp. 326\u2013327 (1985)","DOI":"10.1109\/CDC.1985.268857"},{"key":"1845_CR26","first-page":"216","volume":"113","author":"K Srinivasan","year":"1990","unstructured":"Srinivasan, K., Shaw, F.R.: Analysis and design of repetitive control systems using the regeneration spectrum. Am. Control Conf. 113, 216 (1990)","journal-title":"Am. Control Conf."}],"container-title":["Journal of Intelligent & Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-023-01845-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-023-01845-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-023-01845-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T05:07:36Z","timestamp":1685336856000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-023-01845-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["1845"],"URL":"https:\/\/doi.org\/10.1007\/s10846-023-01845-y","relation":{},"ISSN":["0921-0296","1573-0409"],"issn-type":[{"value":"0921-0296","type":"print"},{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5]]},"assertion":[{"value":"30 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This study did not involve human or animal subjects.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to Participate"}},{"value":"The authors confirm that human study participants provided informed consent for all images published.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}},{"value":"The authors declared that they have no conflicts of interest to this work.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"3"}}