{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T16:20:26Z","timestamp":1790785226409,"version":"4.1.0"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T00:00:00Z","timestamp":1687824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51975566"],"award-info":[{"award-number":["51975566"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Engineering with Computers"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s00366-023-01866-z","type":"journal-article","created":{"date-parts":[[2023,6,27]],"date-time":"2023-06-27T15:18:36Z","timestamp":1687879116000},"page":"1217-1230","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Modeling of continuum robots with environmental constraints"],"prefix":"10.1007","volume":"40","author":[{"given":"Peng","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuwang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tingwen","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenping","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,6,27]]},"reference":[{"issue":"7553","key":"1866_CR1","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1038\/nature14543","volume":"521","author":"D Rus","year":"2015","unstructured":"Rus D, Tolley MT (2015) Design, fabrication and control of soft robots. Nature 521(7553):467\u2013475","journal-title":"Nature"},{"issue":"1","key":"1866_CR2","doi-asserted-by":"publisher","first-page":"642","DOI":"10.1109\/TIE.2021.3053887","volume":"69","author":"G Hwang","year":"2022","unstructured":"Hwang G, Park J, Cortes D, Hyeon K, Kyung K (2022) Electroadhesion-based high-payload soft gripper with mechanically strengthened structure. IEEE Trans Ind Electron 69(1):642\u2013651","journal-title":"IEEE Trans Ind Electron"},{"issue":"4","key":"1866_CR3","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1089\/soro.2018.0154","volume":"7","author":"H Li","year":"2018","unstructured":"Li H, Yao J, Liu C, Zhou P, Xu Y, Zhao Y (2018) A bioinspired soft swallowing robot based on compliant guiding structure. Soft Robot 7(4):491\u2013499","journal-title":"Soft Robot"},{"issue":"8","key":"1866_CR4","doi-asserted-by":"publisher","first-page":"3028","DOI":"10.1126\/scirobotics.aan3028","volume":"2","author":"EW Hawkes","year":"2017","unstructured":"Hawkes EW, Blumenschein LH, Greer JD, Okamura AM (2017) A soft robot that navigates its environment through growth. Sci Robot 2(8):3028","journal-title":"Sci Robot"},{"issue":"4","key":"1866_CR5","doi-asserted-by":"publisher","first-page":"3303","DOI":"10.1109\/TIE.2020.2978728","volume":"68","author":"G Pang","year":"2021","unstructured":"Pang G, Yang G, Heng W, Ye Z, Huang X, Yang H, Pang Z (2021) CoboSkin: soft robot skin with variable stiffness for safer human\u2013robot collaboration. IEEE Trans Ind Electron 68(4):3303\u20133314","journal-title":"IEEE Trans Ind Electron"},{"issue":"1","key":"1866_CR6","doi-asserted-by":"publisher","first-page":"3690","DOI":"10.1126\/scirobotics.aah3690","volume":"1","author":"C Laschi","year":"2016","unstructured":"Laschi C, Mazzolai B, Cianchetti M (2016) Soft robotics: technologies and systems pushing the boundaries of robot abilities. Sci Robot 1(1):3690","journal-title":"Sci Robot"},{"issue":"1","key":"1866_CR7","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1089\/soro.2018.0034","volume":"6","author":"DG Joseph","year":"2019","unstructured":"Joseph DG, Tania KM, Allison MO, Elliot WH, Soft A (2019) Steerable continuum robot that grows via tip extension. Soft Robot 6(1):95\u2013108","journal-title":"Soft Robot"},{"issue":"33","key":"1866_CR8","doi-asserted-by":"publisher","first-page":"7329","DOI":"10.1126\/scirobotics.aax7329","volume":"4","author":"Y Kim","year":"2019","unstructured":"Kim Y, Parada GA, Liu S, Zhao X (2019) Ferromagnetic continuum robots. Sci Robot 4(33):7329","journal-title":"Sci Robot"},{"issue":"5","key":"1866_CR9","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1089\/soro.2018.0007","volume":"5","author":"AA Shabana","year":"2018","unstructured":"Shabana AA (2018) Continuum-based geometry\/analysis approach for flexible and soft robotic systems. Soft Robot 5(5):613\u2013621","journal-title":"Soft Robot"},{"issue":"5","key":"1866_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TRO.2014.2325992","volume":"30","author":"F Renda","year":"2014","unstructured":"Renda F, Giorelli M, Calisti M, Cianchetti M (2014) Dynamic model of a multibending soft robot arm driven by cables. IEEE Trans Robot 30(5):1\u201314","journal-title":"IEEE Trans Robot"},{"issue":"6","key":"1866_CR11","doi-asserted-by":"publisher","first-page":"1518","DOI":"10.1109\/TRO.2018.2868815","volume":"34","author":"F Renda","year":"2018","unstructured":"Renda F, Boyer F, Dias J, Seneviratne L (2018) Discrete Cosserat approach for multisection soft manipulator dynamics. IEEE Trans Robot 34(6):1518\u20131533","journal-title":"IEEE Trans Robot"},{"issue":"5","key":"1866_CR12","doi-asserted-by":"publisher","first-page":"768","DOI":"10.1177\/0278364913518998","volume":"33","author":"MG Catalano","year":"2014","unstructured":"Catalano MG, Grioli G, Farnioli E, Serio A, Piazza C, Bicchi A (2014) Adaptive synergies for the design and control of the Pisa\/IIT SoftHand. Int J Robot Res 33(5):768\u2013782","journal-title":"Int J Robot Res"},{"issue":"8","key":"1866_CR13","doi-asserted-by":"publisher","first-page":"6108","DOI":"10.1109\/TIE.2018.2872005","volume":"66","author":"H Yang","year":"2019","unstructured":"Yang H, Xu M, Li W, Zhang S (2019) Design and implementation of a soft robotic arm driven by SMA coils. IEEE Trans Ind Electron 66(8):6108\u20136116","journal-title":"IEEE Trans Ind Electron"},{"issue":"1","key":"1866_CR14","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1109\/TRO.2013.2281564","volume":"30","author":"WS Rone","year":"2014","unstructured":"Rone WS, Ben-Tzvi P (2014) Continuum robot dynamics utilizing the principle of virtual power. IEEE Trans Robot 30(1):275\u2013287","journal-title":"IEEE Trans Robot"},{"issue":"3","key":"1866_CR15","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3182\/8\/3\/036008","volume":"8","author":"R Kang","year":"2013","unstructured":"Kang R, Branson DT, Zheng T, Guglielmino E, Caldwell DG (2013) Design, modeling and control of a pneumatically actuated manipulator inspired by biological continuum structures. Bioinspir Biomim 8(3):036008","journal-title":"Bioinspir Biomim"},{"issue":"2","key":"1866_CR16","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1109\/TMECH.2016.2636199","volume":"22","author":"R Kang","year":"2016","unstructured":"Kang R, Guo Y, Chen L, Branson DT, Dai JS (2016) Design of a pneumatic muscle based continuum robot with embedded tendons. IEEE-ASME Trans Mechatron 22(2):751\u2013761","journal-title":"IEEE-ASME Trans Mechatron"},{"key":"1866_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2021.104429","volume":"165","author":"J Yang","year":"2021","unstructured":"Yang J, Peng H, Zhou W, Zhang J, Wu Z (2021) A modular approach for dynamic modeling of multisegment continuum robots. Mech Mach Theory 165:104429","journal-title":"Mech Mach Theory"},{"issue":"13","key":"1866_CR18","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1177\/0278364910368147","volume":"29","author":"RJ Webster","year":"2010","unstructured":"Webster RJ, Jones BA (2010) Design and kinematic modeling of constant curvature continuum robots: a review. Int J Robot Res 29(13):1661\u20131683","journal-title":"Int J Robot Res"},{"key":"1866_CR19","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.mechmachtheory.2019.02.005","volume":"135","author":"H Yuan","year":"2019","unstructured":"Yuan H, Zhou L, Xu W (2019) A comprehensive static model of cable-driven multi-section continuum robots considering friction effect. Mech Mach Theory 135:130\u2013149","journal-title":"Mech Mach Theory"},{"issue":"6","key":"1866_CR20","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1109\/TRO.2015.2489500","volume":"31","author":"J Burgner-Kahrs","year":"2015","unstructured":"Burgner-Kahrs J, Rucker DC, Choset H (2015) Continuum robots for medical applications: a survey. IEEE Trans Robot 31(6):1261\u20131280","journal-title":"IEEE Trans Robot"},{"issue":"6","key":"1866_CR21","doi-asserted-by":"publisher","first-page":"2812","DOI":"10.1109\/TMECH.2020.2993543","volume":"25","author":"HD Yang","year":"2020","unstructured":"Yang HD, Asbeck AT (2020) Design and characterization of a modular hybrid continuum robotics manipulator. IEEE-ASME Trans Mechatron 25(6):2812\u20132823","journal-title":"IEEE-ASME Trans Mechatron"},{"key":"1866_CR22","doi-asserted-by":"crossref","unstructured":"Misher MK, Samantaray AK, Chakraborty G, Jain A, Pathak P, Merzouki R (2019) Dynamic modelling of an elephant trunk like flexible bionic manipulator. In: Proceedings of the ASME 2019 international mechanical engineering congress and exposition (IMECE)","DOI":"10.1115\/IMECE2019-11113"},{"key":"1866_CR23","doi-asserted-by":"crossref","unstructured":"Greer JD, Morimoto TK, Okamura AM, Hawkes EW (2017) Series pneumatic artificial muscles (sPAMs) and application to a soft continuum robot. In: 2017 IEEE international conference on robotics and automation (ICRA). IEEE, pp 5503\u20135510","DOI":"10.1109\/ICRA.2017.7989648"},{"issue":"1","key":"1866_CR24","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1089\/soro.2018.0034","volume":"6","author":"JD Greer","year":"2019","unstructured":"Greer JD, Morimoto TK, Okamura AM, Hawkes EW, Soft A (2019) Steerable continuum robot that grows via tip extension. Soft Robot 6(1):95\u2013108","journal-title":"Soft Robot"},{"issue":"7","key":"1866_CR25","doi-asserted-by":"publisher","first-page":"840","DOI":"10.1177\/0278364915587925","volume":"35","author":"AD Marchese","year":"2015","unstructured":"Marchese AD, Rus D (2015) Design, kinematics, and control of a soft spatial fluidic elastomer manipulator. Int J Robot Res 35(7):840\u2013869","journal-title":"Int J Robot Res"},{"issue":"1","key":"1866_CR26","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1109\/TRO.2008.2006868","volume":"25","author":"RJ Webster","year":"2009","unstructured":"Webster RJ, Romano JM, Cowan NJ (2009) Mechanics of precurved-tube continuum robots. IEEE Trans Robot 25(1):67\u201378","journal-title":"IEEE Trans Robot"},{"issue":"10","key":"1866_CR27","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.1177\/0278364910367543","volume":"29","author":"DC Rucker","year":"2010","unstructured":"Rucker DC, Webster RJ, Chirikjian GS (2010) Equilibrium conformations of concentric\u2014tube continuum robots. Int J Robot Res 29(10):1263\u20131280","journal-title":"Int J Robot Res"},{"issue":"2","key":"1866_CR28","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1109\/TMECH.2014.2313741","volume":"20","author":"C Escande","year":"2014","unstructured":"Escande C, Chettibi T, Merzouki R, Coelen V, Pathak PM (2014) Kinematic calibration of a multisection bionic manipulator. IEEE-ASME Trans Mechatron 20(2):663\u2013674","journal-title":"IEEE-ASME Trans Mechatron"},{"issue":"1","key":"1866_CR29","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1177\/0278364920917203","volume":"40","author":"Z Gong","year":"2020","unstructured":"Gong Z, Fang X, Chen X, Cheng J, Xie Z, Liu J, Chen B, Yang H, Kong S, Hao Y, Wang T, Yu J, Wen L (2020) A soft manipulator for efficient delicate grasping in shallow water: modeling, control, and real-world experiments. Int J Robot Res 40(1):449\u2013469","journal-title":"Int J Robot Res"},{"issue":"14","key":"1866_CR30","doi-asserted-by":"publisher","first-page":"1620","DOI":"10.1177\/0278364920913929","volume":"39","author":"C Yang","year":"2020","unstructured":"Yang C, Geng S, Walker I, Branson DT, Liu J, Dai J, Kang R (2020) Geometric constraint-based modeling and analysis of a novel continuum robot with shape memory alloy initiated variable stiffness. Int J Robot Res 39(14):1620\u20131634","journal-title":"Int J Robot Res"},{"issue":"3","key":"1866_CR31","doi-asserted-by":"publisher","DOI":"10.1088\/1748-3190\/10\/3\/035002","volume":"10","author":"S Godage","year":"2015","unstructured":"Godage S, Medrano-Cerda GA, Branson DT, Guglielmino E, Caldwell DG (2015) Modal kinematics for multisection continuum arms. Bioinspir Biomim 10(3):035002","journal-title":"Bioinspir Biomim"},{"key":"1866_CR32","doi-asserted-by":"crossref","unstructured":"Gonthina PS, Kapadia AD, Godage IS, Walker ID (2019) Modeling variable curvature parallel continuum robots using Euler curves. In: 2019 International conference on robotics and automation (ICRA), pp 1679\u20131685","DOI":"10.1109\/ICRA.2019.8794238"},{"issue":"4","key":"1866_CR33","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1089\/soro.2017.0111","volume":"5","author":"I Singh","year":"2018","unstructured":"Singh I, Amara Y, Melingui A, Mani Pathak P, Merzouki R (2018) Modeling of continuum manipulators using pythagorean hodograph curves. Soft Robot 5(4):425\u2013442","journal-title":"Soft Robot"},{"issue":"3","key":"1866_CR34","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1089\/soro.2017.0079","volume":"5","author":"TM Bieze","year":"2018","unstructured":"Bieze TM, Largilliere F, Kruszewski A, Zhang Z, Merzouki R, Duriez C (2018) Finite element method-based kinematics and closedloop control of soft, continuum manipulators. Soft Robot 5(3):348\u2013364","journal-title":"Soft Robot"},{"issue":"6","key":"1866_CR35","doi-asserted-by":"publisher","first-page":"3175","DOI":"10.1109\/TMECH.2021.3055339","volume":"26","author":"X Huang","year":"2021","unstructured":"Huang X, Zou J, Gu G (2021) Kinematic modeling and control of variable curvature continuum robots. IEEE-ASME Trans Mechatron 26(6):3175\u20133185","journal-title":"IEEE-ASME Trans Mechatron"},{"issue":"3","key":"1866_CR36","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1089\/soro.2015.0006","volume":"2","author":"S Godage","year":"2015","unstructured":"Godage S, Wirz R, Walker ID, Webster RJ (2015) Accurate and efficient dynamics for variable-length continuum arms: a center of gravity approach. Soft Robot 2(3):96\u2013106","journal-title":"Soft Robot"},{"issue":"3","key":"1866_CR37","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1109\/LRA.2017.2669367","volume":"2","author":"E Coevoet","year":"2017","unstructured":"Coevoet E, Escande A, Duriez C (2017) Optimization-based inverse model of soft robots with contact handling. IEEE Robot Autom Let 2(3):1413\u20131419","journal-title":"IEEE Robot Autom Let"},{"key":"1866_CR38","doi-asserted-by":"crossref","unstructured":"Pall E,Sieverling A, Brock O (2018) Contingent contact-based motion planning. In: IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 6615\u20136621","DOI":"10.1109\/IROS.2018.8594365"},{"key":"1866_CR39","doi-asserted-by":"crossref","unstructured":"Sieverling A, Eppner C, Wolff F, Brock O (2017) Interleaving motion in contact and in free space for planning under uncertainty. In: IEEE\/RSJ international conference on intelligent robots and systems (IROS), pp 4011\u20134073","DOI":"10.1109\/IROS.2017.8206255"},{"issue":"2","key":"1866_CR40","doi-asserted-by":"publisher","first-page":"1852","DOI":"10.1109\/LRA.2019.2898047","volume":"4","author":"Z Zhang","year":"2019","unstructured":"Zhang Z, Dequidt J, Back J, Liu H, Duriez C (2019) Motion control of cable-driven continuum catheter robot through contacts. IEEE Robot Autom Lett 4(2):1852\u20131859","journal-title":"IEEE Robot Autom Lett"},{"issue":"4","key":"1866_CR41","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1109\/TRO.2014.2309194","volume":"30","author":"MC Yip","year":"2014","unstructured":"Yip MC, Camarillo DB (2014) Model-less feedback control of continuum manipulators in constrained environments. IEEE Trans Robot 30(4):880\u2013889","journal-title":"IEEE Trans Robot"},{"issue":"3","key":"1866_CR42","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1089\/soro.2019.0095","volume":"8","author":"Y Chen","year":"2021","unstructured":"Chen Y, Wang L, Galloway K, Godage I, Simaan N, Barth E (2021) Modal-based kinematics and contact detection of soft robots. Soft Robot 8(3):298\u2013309","journal-title":"Soft Robot"},{"issue":"4","key":"1866_CR43","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1177\/0278364919897292","volume":"39","author":"C DellaSantina","year":"2020","unstructured":"DellaSantina C, Katzschmann RK, Bicchi A, Rus D (2020) Model-based dynamic feedback control of a planar soft robot: trajectory tracking and interaction with the environment. Int J Robot Res 39(4):490\u2013513","journal-title":"Int J Robot Res"},{"issue":"14","key":"1866_CR44","doi-asserted-by":"publisher","first-page":"1724","DOI":"10.1177\/0278364920903774","volume":"39","author":"D Greer","year":"2020","unstructured":"Greer D, Blumenschein LH, Alterovitz R, Hawkes EW, Okamura AM (2020) Robust navigation of a soft growing robot by exploiting contact with the environment. Int J Robot Res 39(14):1724\u20131738","journal-title":"Int J Robot Res"},{"key":"1866_CR45","doi-asserted-by":"crossref","unstructured":"Merzouki R, Samantaray AK, Pathak PM, Ould Bouamama B (2013) Rigid body, flexible body and micro electromechanical systems. In: Intelligent mechatronic systems: modelling, control and diagnosis. Springer London, UK, pp 313\u2013315","DOI":"10.1007\/978-1-4471-4628-5"},{"key":"1866_CR46","doi-asserted-by":"crossref","unstructured":"Li S, Vogt DM, Rus D, Wood RJ (2017) Fluid-driven origami-inspired artificial muscles. In: Proceedings of the National Academy of Sciences of the United States of America (PNAS), pp 13132\u201313137","DOI":"10.1073\/pnas.1713450114"},{"issue":"1","key":"1866_CR47","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1089\/soro.2018.0063","volume":"6","author":"G Lee","year":"2019","unstructured":"Lee G, Rodrigue H (2019) Origami-based vacuum pneumatic artificial muscles with large contraction ratios. Soft Robot 6(1):109\u2013117","journal-title":"Soft Robot"}],"container-title":["Engineering with Computers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01866-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00366-023-01866-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00366-023-01866-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T02:51:13Z","timestamp":1713667873000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00366-023-01866-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,27]]},"references-count":47,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["1866"],"URL":"https:\/\/doi.org\/10.1007\/s00366-023-01866-z","relation":{},"ISSN":["0177-0667","1435-5663"],"issn-type":[{"value":"0177-0667","type":"print"},{"value":"1435-5663","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,27]]},"assertion":[{"value":"20 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 June 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 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 they have no confict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}