{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T19:47:00Z","timestamp":1769197620766,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T00:00:00Z","timestamp":1687737600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T00:00:00Z","timestamp":1687737600000},"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":["Neural Comput & Applic"],"published-print":{"date-parts":[[2024,2]]},"DOI":"10.1007\/s00521-023-08755-y","type":"journal-article","created":{"date-parts":[[2023,6,26]],"date-time":"2023-06-26T06:02:21Z","timestamp":1687759341000},"page":"2231-2244","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["State estimation of hydraulic quadruped robots using invariant-EKF and kinematics with neural networks"],"prefix":"10.1007","volume":"36","author":[{"given":"Shangru","family":"Yang","sequence":"first","affiliation":[]},{"given":"Qingjun","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Rui","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Zhenyang","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Congfei","family":"Li","sequence":"additional","affiliation":[]},{"given":"Hu","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,26]]},"reference":[{"key":"8755_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/9781316671528","volume-title":"State estimation for robotics","author":"TD Barfoot","year":"2017","unstructured":"Barfoot TD (2017) State estimation for robotics. Cambridge University Press"},{"issue":"4","key":"8755_CR2","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.1109\/TRO.2018.2853729","volume":"34","author":"T Qin","year":"2018","unstructured":"Qin T, Li P, Shen S (2018) Vins-mono: a robust and versatile monocular visual-inertial state estimator. IEEE Trans Robot 34(4):1004\u20131020","journal-title":"IEEE Trans Robot"},{"key":"8755_CR3","doi-asserted-by":"crossref","unstructured":"Ye H, Chen Y, Liu M (2019) Tightly coupled 3d lidar inertial odometryand mapping. In: 2019 international conference on robotics and automation (ICRA), pp 3144\u20133150, IEEE","DOI":"10.1109\/ICRA.2019.8793511"},{"issue":"2","key":"8755_CR4","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1109\/LRA.2018.2793349","volume":"3","author":"K Sun","year":"2018","unstructured":"Sun K, Mohta K, Pfrommer B, Watterson M, Liu S, Mulgaonkar Y, Taylor CJ, Kumar V (2018) Robust stereo visual inertial odometry for fast autonomous flight. IEEE Robot Autom Lett 3(2):965\u2013972","journal-title":"IEEE Robot Autom Lett"},{"key":"8755_CR5","doi-asserted-by":"crossref","unstructured":"Gehring C, Coros S, Hutter M, Bloesch M, Hoepflinger MA, Siegwart R (2013) Control of dynamic gaits for a quadrupedal robot. In: 2013 IEEE international conference on robotics and automation, pp 3287\u20133292, IEEE","DOI":"10.1109\/ICRA.2013.6631035"},{"key":"8755_CR6","doi-asserted-by":"crossref","unstructured":"Gehring C, Coros S, Hutter M, Bloesch M, Fankhauser P, Hoepflinger MA, Siegwart R (2014) Towards automatic discovery of agilegaits for quadrupedal robot. In: 2014 IEEE international conference on robotics and automation (ICRA), pp 4243\u20134248, IEEE","DOI":"10.1109\/ICRA.2014.6907476"},{"key":"8755_CR7","doi-asserted-by":"crossref","unstructured":"Bloesch M, Gehring C, Fankhauser P, Hutter M, Hoepflinger MA, Siegwart R (2013) State estimation for legged robots on unstable and slippery terrain. In: 2013 IEEE\/RSJ international conference on intel- ligent robots and systems, pp 6058\u20136064, IEEE","DOI":"10.1109\/IROS.2013.6697236"},{"key":"8755_CR8","doi-asserted-by":"publisher","first-page":"17","DOI":"10.7551\/mitpress\/9816.003.0008","volume":"17","author":"M Bloesch","year":"2013","unstructured":"Bloesch M, Hutter M, Hoepflinger MA, Leutenegger S, Gehring C, Remy CD, Siegwart R (2013) State estimation for legged robots- consistent fusion of leg kinematics and imu. Robotics 17:17\u201324","journal-title":"Robotics"},{"key":"8755_CR9","doi-asserted-by":"crossref","unstructured":"Gehring C, Bellicoso CD, Coros S, Bloesch M, Fankhauser P, Hutter M, Siegwart R (2015) Dynamic trotting on slopes for quadrupedal robots. In: 2015 IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 5129\u20135135, IEEE","DOI":"10.1109\/IROS.2015.7354099"},{"key":"8755_CR10","doi-asserted-by":"crossref","unstructured":"Nobili S, Camurri M, Barasuol V, Focchi M, Caldwell DG, Semini C, Fallon MF (2017) Heterogeneous sensor fusion for accurate state estimation of dynamic legged robots. In: Robotics: science and systems","DOI":"10.15607\/RSS.2017.XIII.007"},{"issue":"2","key":"8755_CR11","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1109\/LRA.2017.2652491","volume":"2","author":"M Camurri","year":"2017","unstructured":"Camurri M, Fallon M, Bazeille S, Radulescu A, Barasuol V, Caldwell DG, Semini C (2017) Probabilistic contact estimation and impact detection for state estimation of quadruped robots. IEEE Robot Autom Lett 2(2):1023\u20131030","journal-title":"IEEE Robot Autom Lett"},{"issue":"6","key":"8755_CR12","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1177\/0278364915587333","volume":"35","author":"J Ma","year":"2016","unstructured":"Ma J, Bajracharya M, Susca S, Matthies L, Malchano M (2016) Real- time pose estimation of a dynamic quadruped in gps-denied environ- ments for 24-hour operation. Int J Robot Res 35(6):631\u2013653","journal-title":"Int J Robot Res"},{"key":"8755_CR13","doi-asserted-by":"crossref","unstructured":"Hutter M, Gehring C, Jud D, Lauber A, Bellicoso CD, Tsounis V, Hwangbo J, Bodie K, Fankhauser P, Bloesch M et al (2016) Anymal- a highly mobile and dynamic quadrupedal robot. In: 2016 IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 38\u201344, IEEE","DOI":"10.1109\/IROS.2016.7758092"},{"issue":"4","key":"8755_CR14","doi-asserted-by":"publisher","first-page":"4507","DOI":"10.1109\/LRA.2019.2933768","volume":"4","author":"D Wisth","year":"2019","unstructured":"Wisth D, Camurri M, Fallon M (2019) Robust legged robot state esti- mation using factor graph optimization. IEEE Robot Autom Lett 4(4):4507\u20134514","journal-title":"IEEE Robot Autom Lett"},{"issue":"1","key":"8755_CR15","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1109\/LRA.2017.2776340","volume":"3","author":"M Bloesch","year":"2017","unstructured":"Bloesch M, Burri M, Sommer H, Siegwart R, Hutter M (2017) The two-state implicit filter recursive estimation for mobile robots. IEEE Robot Autom Lett 3(1):573\u2013580","journal-title":"IEEE Robot Autom Lett"},{"key":"8755_CR16","doi-asserted-by":"crossref","unstructured":"Park H-W, Wensing PM, Kim S et al (2015) Online planning for autonomous running jumps over obstacles in high-speed quadrupeds","DOI":"10.15607\/RSS.2015.XI.047"},{"key":"8755_CR17","doi-asserted-by":"publisher","first-page":"68","DOI":"10.3389\/frobt.2020.00068","volume":"7","author":"M Camurri","year":"2020","unstructured":"Camurri M, Ramezani M, Nobili S, Fallon M (2020) Pronto: A multi-sensor state estimator for legged robots in real-world scenarios. Front Robot AI 7:68","journal-title":"Front Robot AI"},{"key":"8755_CR18","doi-asserted-by":"crossref","unstructured":"Chilian A, Hirschmuller H, Gorner M (2011) Multisensor data fusion for robust pose estimation of a six-legged walking robot. In: 2011 IEEE\/RSJ international conference on intelligent robots and systems, pp 2497\u20132504, IEEE","DOI":"10.1109\/IROS.2011.6048125"},{"issue":"2","key":"8755_CR19","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1109\/TAC.2014.2342911","volume":"60","author":"A Barrau","year":"2014","unstructured":"Barrau A, Bonnabel S (2014) Intrinsic filtering on lie groups with applications to attitude estimation. IEEE Trans Autom Control 60(2):436\u2013449","journal-title":"IEEE Trans Autom Control"},{"key":"8755_CR20","unstructured":"Barrau A, Bonnabel S (2015) An ekf-slam algorithm with consistency properties. arXiv preprint arXiv:1510.06263"},{"issue":"4","key":"8755_CR21","doi-asserted-by":"publisher","first-page":"1797","DOI":"10.1109\/TAC.2016.2594085","volume":"62","author":"A Barrau","year":"2016","unstructured":"Barrau A, Bonnabel S (2016) The invariant extended kalman filter as a stable observer. IEEE Trans Autom Control 62(4):1797\u20131812","journal-title":"IEEE Trans Autom Control"},{"key":"8755_CR22","doi-asserted-by":"crossref","unstructured":"Barrau A, Bonnabel S (2018) Stochastic observers on lie groups: a tutorial. In: 2018 IEEE conference on decision and control (CDC), pp 1264\u20131269, IEEE","DOI":"10.1109\/CDC.2018.8618988"},{"key":"8755_CR23","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1146\/annurev-control-060117-105010","volume":"1","author":"A Barrau","year":"2018","unstructured":"Barrau A, Bonnabel S (2018) Invariant kalman filtering. Annu Rev Control Robot Auton Syst 1:237\u2013257","journal-title":"Annu Rev Control Robot Auton Syst"},{"key":"8755_CR24","doi-asserted-by":"crossref","unstructured":"Wu K, Zhang T, Su D, Huang S, Dissanayake G (2017) An invariant- ekf vins algorithm for improving consistency. In: 2017 IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 1578\u20131585, IEEE","DOI":"10.1109\/IROS.2017.8205965"},{"key":"8755_CR25","doi-asserted-by":"crossref","unstructured":"Hartley R, Jadidi MG, Grizzle JW, Eustice RM (2018) Contact-aided invariant extended kalman filtering for legged robot state estimation. In: Robotics: science and systems","DOI":"10.15607\/RSS.2018.XIV.050"},{"issue":"4","key":"8755_CR26","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1177\/0278364919894385","volume":"39","author":"R Hartley","year":"2020","unstructured":"Hartley R, Ghaffari M, Eustice RM, Grizzle JW (2020) Contact-aided invariant extended kalman filtering for robot state estimation. Int J Robot Res 39(4):402\u2013430","journal-title":"Int J Robot Res"},{"key":"8755_CR27","doi-asserted-by":"crossref","unstructured":"Hartley R, Jadidi MG, Gan L, Huang J-K, Grizzle JW, Eustice RM (2018) Hybrid contact preintegration for visual-inertial-contact state estimation using factor graphs. In: 2018 IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 3783\u20133790, IEEE","DOI":"10.1109\/IROS.2018.8593801"},{"key":"8755_CR28","doi-asserted-by":"crossref","unstructured":"Hartley R, MangelsonJ, Gan L, Jadidi MG, Walls JM, Eustice RM, Grizzle JW (2018) Legged robot state-estimation through combined forward kinematic and preintegrated contact factors. In: 2018 IEEE international conference on robotics and automation (ICRA), pp 4422\u20134429, IEEE","DOI":"10.1109\/ICRA.2018.8460748"},{"key":"8755_CR29","doi-asserted-by":"crossref","unstructured":"Chauchat P, Barrau A, Bonnabel S (2018) Invariant smoothing on lie groups. In: 2018 IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 1703\u20131710, IEEE","DOI":"10.1109\/IROS.2018.8594068"},{"issue":"2","key":"8755_CR30","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1109\/TRO.2012.2228309","volume":"29","author":"M Reinstein","year":"2012","unstructured":"Reinstein M, Hoffmann M (2012) Dead reckoning in a dynamic quadruped robot based on multimodal proprioceptive sensory informa- tion. IEEE Trans Rob 29(2):563\u2013571","journal-title":"IEEE Trans Rob"},{"key":"8755_CR31","doi-asserted-by":"crossref","unstructured":"Rotella N, Schaal S, Righetti L (2018) Unsupervised contact learning for humanoid estimation and control. In: 2018 IEEE International Conference on Robotics and Automation (ICRA), pp 411\u2013417, IEEE","DOI":"10.1109\/ICRA.2018.8462864"},{"key":"8755_CR32","doi-asserted-by":"crossref","unstructured":"Piperakis S, Timotheatos S, Trahanias P (2019) Unsupervised gait phase estimation for humanoid robot walking. In: 2019 International conference on robotics and automation (ICRA), pp 270\u2013276, IEEE","DOI":"10.1109\/ICRA.2019.8793598"},{"key":"8755_CR33","unstructured":"Buchanan R, Camurri M, Dellaert F, Fallon M (2022) Learning inertial odometry for dynamic legged robot state estimation. In: Conference on robot learning, pp 1575\u20131584, PMLR"},{"issue":"1","key":"8755_CR34","doi-asserted-by":"publisher","DOI":"10.1115\/1.4045154","volume":"142","author":"Q Yang","year":"2020","unstructured":"Yang Q, Zhu R, Niu Z, Chen C, Mao Q, Zheng Y (2020) Natural frequency analysis of hydraulic quadruped robot and structural opti- mization of the leg. J Dyn Syst Meas Contr 142(1):011009","journal-title":"J Dyn Syst Meas Contr"},{"issue":"4","key":"8755_CR35","doi-asserted-by":"publisher","first-page":"1336","DOI":"10.1007\/s12555-021-0235-5","volume":"20","author":"R Zhu","year":"2022","unstructured":"Zhu R, Yang Q, Liu Y, Dong R, Jiang C, Song J (2022) Sliding mode robust control of hydraulic drive unit of hydraulic quadruped robot. Int J Control Autom Syst 20(4):1336\u20131350","journal-title":"Int J Control Autom Syst"},{"issue":"5","key":"8755_CR36","doi-asserted-by":"publisher","first-page":"1931","DOI":"10.1007\/s12555-020-0221-3","volume":"19","author":"R Zhu","year":"2021","unstructured":"Zhu R, Yang Q, Song J, Yang S, Liu Y, Mao Q (2021) Research and improvement on active compliance control of hydraulic quadruped robot. Int J Control Autom Syst 19(5):1931\u20131943","journal-title":"Int J Control Autom Syst"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-023-08755-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00521-023-08755-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-023-08755-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T15:04:08Z","timestamp":1705676648000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00521-023-08755-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,26]]},"references-count":36,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,2]]}},"alternative-id":["8755"],"URL":"https:\/\/doi.org\/10.1007\/s00521-023-08755-y","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,26]]},"assertion":[{"value":"17 January 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 June 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":"The authors declare that there are no conflicts of interest regarding the publication of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}