{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T08:18:32Z","timestamp":1772007512279,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T00:00:00Z","timestamp":1656028800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T00:00:00Z","timestamp":1656028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1813221"],"award-info":[{"award-number":["U1813221"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research and Development Program of China","award":["2019YFB1311200"],"award-info":[{"award-number":["2019YFB1311200"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s10846-022-01672-7","type":"journal-article","created":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T14:02:46Z","timestamp":1656079366000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["CRRIK: A Fast Heuristic Algorithm for the Inverse Kinematics of Continuum Robot"],"prefix":"10.1007","volume":"105","author":[{"given":"Haoran","family":"Wu","sequence":"first","affiliation":[]},{"given":"Jingjun","family":"Yu","sequence":"additional","affiliation":[]},{"given":"Jie","family":"Pan","sequence":"additional","affiliation":[]},{"given":"Guoxin","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8585-0703","authenticated-orcid":false,"given":"Xu","family":"Pei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,24]]},"reference":[{"key":"1672_CR1","doi-asserted-by":"publisher","unstructured":"Pritts, M. B., & Rahn, C. D.: Design of an artificial muscle continuum robot. In IEEE international conference on robotics and automation, 2004. Proceedings. ICRA'04. 2004 5, 4742-4746. IEEE (2004). https:\/\/doi.org\/10.1109\/ROBOT.2004.1302467","DOI":"10.1109\/ROBOT.2004.1302467"},{"key":"#cr-split#-1672_CR2.1","unstructured":"Chikhaoui, M. T., & Burgner-Kahrs, J.: Control of Continuum Robots for Medical Applications: State of the Art. In ACTUATOR 2018"},{"key":"#cr-split#-1672_CR2.2","unstructured":"16th International Conference on New Actuators (pp. 1-11). VDE, (2018)"},{"key":"1672_CR3","doi-asserted-by":"publisher","unstructured":"Walker, I. D.: Continuous backbone \u201ccontinuum\u201d robot manipulators. International Scholarly Research Notices, 2013, (2013). https:\/\/doi.org\/10.5402\/2013\/726506","DOI":"10.5402\/2013\/726506"},{"issue":"6","key":"1672_CR4","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, D.C., Choset, H.: Continuum robots for medical applications: a survey. IEEE Trans. Robot. 31(6), 1261\u20131280 (2015). https:\/\/doi.org\/10.1109\/TRO.2015.2489500","journal-title":"IEEE Trans. Robot."},{"key":"1672_CR5","doi-asserted-by":"publisher","unstructured":"Wolf, A., Brown, H. B., Casciola, R., Costa, A., Schwerin, M., Shamas, E., & Choset, H.: A mobile hyper redundant mechanism for search and rescue tasks. In proceedings 2003 IEEE\/RSJ international conference on intelligent robots and systems (IROS 2003) (cat. No. 03CH37453) 3, 2889-2895. IEEE, (2003). https:\/\/doi.org\/10.1109\/IROS.2003.1249309","DOI":"10.1109\/IROS.2003.1249309"},{"key":"1672_CR6","doi-asserted-by":"publisher","unstructured":"Buckingham, R., & Graham, A.: Nuclear snake-arm robots. Industrial Robot: An International Journal, (2012). https:\/\/doi.org\/10.1108\/01439911211192448","DOI":"10.1108\/01439911211192448"},{"key":"1672_CR7","doi-asserted-by":"publisher","unstructured":"Buckingham, R., Chitrakaran, V., Conkie, R., Ferguson, G., Graham, A., Lazell, A., ... , Green, B: Snake-arm robots: a new approach to aircraft assembly (no. 2007-01-3870). SAE Technical Paper. (2007).\u00a0https:\/\/doi.org\/10.4271\/2007-01-3870","DOI":"10.4271\/2007-01-3870"},{"key":"1672_CR8","doi-asserted-by":"publisher","unstructured":"Jones, B. A., & Walker, I. D.: A new approach to Jacobian formulation for a class of multi-section continuum robots. In proceedings of the 2005 IEEE international conference on robotics and automation (pp. 3268-3273). IEEE, (2005). https:\/\/doi.org\/10.1109\/ROBOT.2005.1570614","DOI":"10.1109\/ROBOT.2005.1570614"},{"key":"1672_CR9","doi-asserted-by":"crossref","unstructured":"Dul\u0119ba, I., Opa\u0142ka, M.: A comparison of Jacobian-based methods of inverse kinematics for serial robot manipulators. Int. J. Appl. Math. Comput. Sci. 23(2), (2013)","DOI":"10.2478\/amcs-2013-0028"},{"key":"1672_CR10","doi-asserted-by":"publisher","unstructured":"Xu, D., Li, E., Liang, Z., & Gao, Z.: Design and tension modeling of a novel cable-driven rigid Snake-like manipulator. J. Intell. Robot. Syst., 1-18, (2020). https:\/\/doi.org\/10.1007\/s10846-019-01115-w","DOI":"10.1007\/s10846-019-01115-w"},{"key":"1672_CR11","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1016\/j.apm.2016.11.005","volume":"46","author":"JT Machado","year":"2017","unstructured":"Machado, J.T., Lopes, A.M.: A fractional perspective on the trajectory control of redundant and hyper-redundant robot manipulators. Appl. Math. Model. 46, 716\u2013726 (2017). https:\/\/doi.org\/10.1016\/j.apm.2016.11.005","journal-title":"Appl. Math. Model."},{"issue":"2","key":"1672_CR12","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1002\/rob.10070","volume":"20","author":"MW Hannan","year":"2003","unstructured":"Hannan, M.W., Walker, I.D.: Kinematics and the implementation of an elephant's trunk manipulator and other continuum style robots. J. Robot. Syst. 20(2), 45\u201363 (2003). https:\/\/doi.org\/10.1002\/rob.10070","journal-title":"J. Robot. Syst."},{"issue":"1","key":"1672_CR13","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1177\/0278364920917203","volume":"40","author":"Z Gong","year":"2021","unstructured":"Gong, Z., Fang, X., Chen, X., Cheng, J., Xie, Z., Liu, J., et al.: A soft manipulator for efficient delicate grasping in shallow water: modeling, control, and real-world experiments. Int. J. Robot. Res. 40(1), 449\u2013469 (2021). https:\/\/doi.org\/10.1177\/0278364920917203","journal-title":"Int. J. Robot. Res."},{"key":"1672_CR14","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.mechmachtheory.2014.01.008","volume":"75","author":"Y Wei","year":"2014","unstructured":"Wei, Y., Jian, S., He, S., Wang, Z.: General approach for inverse kinematics of nR robots. Mech. Mach. Theory. 75, 97\u2013106 (2014). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2014.01.008","journal-title":"Mech. Mach. Theory"},{"issue":"5","key":"1672_CR15","doi-asserted-by":"publisher","first-page":"1746","DOI":"10.1109\/TSMC.2017.2784828","volume":"50","author":"Z Mu","year":"2018","unstructured":"Mu, Z., Yuan, H., Xu, W., Liu, T., Liang, B.: A segmented geometry method for kinematics and configuration planning of spatial hyper-redundant manipulators. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 50(5), 1746\u20131756 (2018). https:\/\/doi.org\/10.1109\/TSMC.2017.2784828","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"issue":"2","key":"1672_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2316\/Journal.206.2015.2.206-4185","volume":"30","author":"O Tutsoy","year":"2015","unstructured":"Tutsoy, O.: CPG based RL algorithm learns to control of a humanoid robot leg. Int. J. Robot. Autom. 30(2), 1\u20137 (2015). https:\/\/doi.org\/10.2316\/Journal.206.2015.2.206-4185","journal-title":"Int. J. Robot. Autom."},{"issue":"11","key":"1672_CR17","doi-asserted-by":"publisher","first-page":"1735","DOI":"10.1177\/0142331216645176","volume":"39","author":"O Tutsoy","year":"2017","unstructured":"Tutsoy, O., Erol Barkana, D., Colak, S.: Learning to balance an NAO robot using reinforcement learning with symbolic inverse kinematic. Trans. Inst. Meas. Control. 39(11), 1735\u20131748 (2017). https:\/\/doi.org\/10.1177\/0142331216645176","journal-title":"Trans. Inst. Meas. Control."},{"key":"1672_CR18","doi-asserted-by":"publisher","unstructured":"Jiang, H., Wang, Z., Liu, X., Chen, X., Jin, Y., You, X., & Chen, X.: A two-level approach for solving the inverse kinematics of an extensible soft arm considering viscoelastic behavior. In 2017 IEEE international conference on robotics and automation (ICRA) (pp. 6127-6133). IEEE, (2017). https:\/\/doi.org\/10.1109\/ICRA.2017.7989727","DOI":"10.1109\/ICRA.2017.7989727"},{"key":"1672_CR19","doi-asserted-by":"publisher","unstructured":"Melingui, A., Merzouki, R., Mbede, J. B., Escande, C., & Benoudjit, N.: Neural networks based approach for inverse kinematic modeling of a compact bionic handling assistant trunk. In 2014 IEEE 23rd international symposium on industrial electronics (ISIE) (pp. 1239-1244). IEEE, (2014). https:\/\/doi.org\/10.1109\/ISIE.2014.6864791","DOI":"10.1109\/ISIE.2014.6864791"},{"issue":"26","key":"1672_CR20","doi-asserted-by":"publisher","first-page":"eaav1488","DOI":"10.1126\/scirobotics.aav1488","volume":"4","author":"TG Thuruthel","year":"2019","unstructured":"Thuruthel, T.G., Shih, B., Laschi, C., Tolley, M.T.: Soft robot perception using embedded soft sensors and recurrent neural networks. Sci. Robot. 4(26), eaav1488 (2019). https:\/\/doi.org\/10.1126\/scirobotics.aav1488","journal-title":"Sci. Robot."},{"issue":"4","key":"1672_CR21","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1080\/2165347X.2013.823362","volume":"16","author":"B Kenwright","year":"2012","unstructured":"Kenwright, B.: Inverse kinematics\u2013cyclic coordinate descent (CCD). Journal of Graphics Tools. 16(4), 177\u2013217 (2012). https:\/\/doi.org\/10.1080\/2165347X.2013.823362","journal-title":"Journal of Graphics Tools"},{"issue":"4","key":"1672_CR22","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1504\/IJCAT.2009.024084","volume":"34","author":"R Mukundan","year":"2009","unstructured":"Mukundan, R.: A robust inverse kinematics algorithm for animating a joint chain. Int. J. Comput. Appl. Technol. 34(4), 303\u2013308 (2009). https:\/\/doi.org\/10.1504\/IJCAT.2009.024084","journal-title":"Int. J. Comput. Appl. Technol."},{"key":"1672_CR23","doi-asserted-by":"publisher","unstructured":"Mahmudi, M., & Kallmann, M.: Feature-Based Locomotion with Inverse Branch Kinematics. In International Conference on Motion in Games (pp. 39-50). Springer, Berlin, Heidelberg, (2011). https:\/\/doi.org\/10.1007\/978-3-642-25090-3_4","DOI":"10.1007\/978-3-642-25090-3_4"},{"key":"1672_CR24","unstructured":"William II, R. L., & Mayhew IV, J. B.: Obstacle-free control of the hyper-redundant nasa inspection manipulator. In Proc. of the Fifth National Conf. on Applied Mechanics and Robotics (pp. 12-15), (1997)"},{"issue":"2","key":"1672_CR25","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/s00371-003-0226-y","volume":"20","author":"J Brown","year":"2004","unstructured":"Brown, J., Latombe, J.C., Montgomery, K.: Real-time knot-tying simulation. Vis. Comput. 20(2), 165\u2013179 (2004). https:\/\/doi.org\/10.1007\/s00371-003-0226-y","journal-title":"Vis. Comput."},{"issue":"1","key":"1672_CR26","first-page":"572","volume":"6","author":"AP Coimbra","year":"2013","unstructured":"Coimbra, A.P., Cris\u00f6stomo, M.M., Ferreira, J.: Position and anti-collision algorithms for a 3D hyper-redundant robot. In Management and Control of Production and Logistics. 6(1), 572\u2013576 (2013)","journal-title":"In Management and Control of Production and Logistics"},{"issue":"1","key":"1672_CR27","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s13534-016-0209-3","volume":"6","author":"CN Cho","year":"2016","unstructured":"Cho, C.N., Jung, H., Son, J., Sohn, D.K., Kim, K.G.: An intuitive control algorithm for a snake-like natural orifice transluminal endoscopic surgery platform: a preliminary simulation study. Biomed. Eng. Lett. 6(1), 39\u201346 (2016). https:\/\/doi.org\/10.1007\/s13534-016-0209-3","journal-title":"Biomed. Eng. Lett."},{"key":"1672_CR28","unstructured":"Muller-Cajar, R., Mukundan, R.: Triangualation-a new algorithm for inverse kinematics. (2007)"},{"issue":"5","key":"1672_CR29","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.gmod.2011.05.003","volume":"73","author":"A Aristidou","year":"2011","unstructured":"Aristidou, A., Lasenby, J.: FABRIK: a fast, iterative solver for the inverse kinematics problem. Graph. Model. 73(5), 243\u2013260 (2011). https:\/\/doi.org\/10.1016\/j.gmod.2011.05.003","journal-title":"Graph. Model."},{"key":"1672_CR30","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.mechmachtheory.2015.04.011","volume":"91","author":"H Ananthanarayanan","year":"2015","unstructured":"Ananthanarayanan, H., Ord\u00f3\u00f1ez, R.: Real-time inverse kinematics of (2n+ 1) DOF hyper-redundant manipulator arm via a combined numerical and analytical approach. Mech. Mach. Theory. 91, 209\u2013226 (2015). https:\/\/doi.org\/10.1016\/j.mechmachtheory.2015.04.011","journal-title":"Mech. Mach. Theory"},{"key":"1672_CR31","doi-asserted-by":"publisher","first-page":"208836","DOI":"10.1109\/ACCESS.2020.3038424","volume":"8","author":"PC Santos","year":"2020","unstructured":"Santos, P.C., Freire, R.C.S., Carvalho, E.A.N., Molina, L., Freire, E.O.: M-FABRIK: a new inverse kinematics approach to mobile manipulator robots based on FABRIK. IEEE Access. 8, 208836\u2013208849 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.3038424","journal-title":"IEEE Access"},{"key":"1672_CR32","doi-asserted-by":"publisher","unstructured":"Abdallah, M. A., Baziyed, M. S., Fareh, R., & Rabie, T.: Tracking control for robotic manipulator based on FABRIK algorithm. In 2018 Advances in Science and Engineering Technology International Conferences (ASET) (pp. 1-5). IEEE, (2018). https:\/\/doi.org\/10.1109\/ICASET.2018.8376844","DOI":"10.1109\/ICASET.2018.8376844"},{"key":"1672_CR33","unstructured":"Kolpashchikov, D. Y., Laptev, N. V., Danilov, V. V., Skirnevskiy, I. P., Manakov, R. A., & Gerget, O. M.: FABRIK-based inverse kinematics for multi-section continuum robots. In 2018 18th International Conference on Mechatronics-Mechatronika (ME) (pp. 1-8). IEEE, (2018)"},{"issue":"1","key":"1672_CR34","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1109\/TRO.2005.861458","volume":"22","author":"BA Jones","year":"2006","unstructured":"Jones, B.A., Walker, I.D.: Kinematics for multisection continuum robots. IEEE Trans. Robot. 22(1), 43\u201355 (2006). https:\/\/doi.org\/10.1109\/TRO.2005.861458","journal-title":"IEEE Trans. Robot."},{"issue":"3","key":"1672_CR35","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1007\/s10846-017-0734-z","volume":"91","author":"A Amouri","year":"2018","unstructured":"Amouri, A., Zaatri, A., Mahfoudi, C.: Dynamic modeling of a class of continuum manipulators in fixed orientation. J. Intell. Robot. Syst. 91(3), 413\u2013424 (2018). https:\/\/doi.org\/10.1007\/s10846-017-0734-z","journal-title":"J. Intell. Robot. Syst."},{"issue":"4","key":"1672_CR36","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1109\/TRO.2014.2314777","volume":"30","author":"T Mahl","year":"2014","unstructured":"Mahl, T., Hildebrandt, A., Sawodny, O.: A variable curvature continuum kinematics for kinematic control of the bionic handling assistant. IEEE Trans. Robot. 30(4), 935\u2013949 (2014). https:\/\/doi.org\/10.1109\/TRO.2014.2314777","journal-title":"IEEE Trans. Robot."},{"issue":"6","key":"1672_CR37","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1109\/TRO.2006.886268","volume":"22","author":"BA Jones","year":"2006","unstructured":"Jones, B.A., Walker, I.D.: Practical kinematics for real-time implementation of continuum robots. IEEE Trans. Robot. 22(6), 1087\u20131099 (2006). https:\/\/doi.org\/10.1109\/TRO.2006.886268","journal-title":"IEEE Trans. Robot."},{"issue":"13","key":"1672_CR38","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1177\/0278364910368147","volume":"29","author":"RJ Webster III","year":"2010","unstructured":"Webster III, R.J., Jones, B.A.: Design and kinematic modeling of constant curvature continuum robots: a review. Int J Robot Res. 29(13), 1661\u20131683 (2010). https:\/\/doi.org\/10.1177\/0278364910368147","journal-title":"Int J Robot Res"},{"key":"1672_CR39","doi-asserted-by":"publisher","unstructured":"Xiong, Z., Tao, J., & Liu, C. (2018). Inverse Kinematics of Hyper-Redundant Snake-Arm Robots with Improved Tip Following Movement. Robot. https:\/\/doi.org\/10.13973\/j.cnki.robot.170255","DOI":"10.13973\/j.cnki.robot.170255"},{"issue":"1","key":"1672_CR40","doi-asserted-by":"publisher","first-page":"172988141775273","DOI":"10.1177\/1729881417752738","volume":"15","author":"C L\u00f3pez-Franco","year":"2018","unstructured":"L\u00f3pez-Franco, C., Hern\u00e1ndez-Barrag\u00e1n, J., Alanis, A.Y., Arana-Daniel, N., L\u00f3pez-Franco, M.: Inverse kinematics of mobile manipulators based on differential evolution. Int. J. Adv. Robot. Syst. 15(1), 1729881417752738 (2018). https:\/\/doi.org\/10.1177\/1729881417752738","journal-title":"Int. J. Adv. Robot. Syst."}],"container-title":["Journal of Intelligent & Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-022-01672-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-022-01672-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-022-01672-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T11:15:05Z","timestamp":1658747705000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-022-01672-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,24]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["1672"],"URL":"https:\/\/doi.org\/10.1007\/s10846-022-01672-7","relation":{},"ISSN":["0921-0296","1573-0409"],"issn-type":[{"value":"0921-0296","type":"print"},{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,24]]},"assertion":[{"value":"30 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to Participate"}},{"value":"The authors declare no competing financial interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"Not applicable","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}}],"article-number":"55"}}