{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,25]],"date-time":"2026-10-25T01:33:38Z","timestamp":1792892018301,"version":"4.5.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T00:00:00Z","timestamp":1729900800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T00:00:00Z","timestamp":1729900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"name":"China Scholarship Council (CSC) for studies at the Institute of Solid Mechanics of Romanian Academy, Roumania","award":["202308130191"],"award-info":[{"award-number":["202308130191"]}]},{"DOI":"10.13039\/501100017526","name":"International Cooperation Project of Ningbo City","doi-asserted-by":"publisher","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}],"id":[{"id":"10.13039\/501100017526","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017526","name":"International Cooperation Project of Ningbo City","doi-asserted-by":"publisher","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}],"id":[{"id":"10.13039\/501100017526","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017526","name":"International Cooperation Project of Ningbo City","doi-asserted-by":"publisher","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}],"id":[{"id":"10.13039\/501100017526","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2019YFB1312500"],"award-info":[{"award-number":["2019YFB1312500"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017610","name":"Shenzhen Science and Technology Innovation Program","doi-asserted-by":"publisher","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}],"id":[{"id":"10.13039\/501100017610","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017610","name":"Shenzhen Science and Technology Innovation Program","doi-asserted-by":"publisher","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}],"id":[{"id":"10.13039\/501100017610","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-024-77137-8","type":"journal-article","created":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T03:01:50Z","timestamp":1729911710000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Upper limb exoskeleton rehabilitation robot inverse kinematics modeling and solution method based on multi-objective optimization"],"prefix":"10.1038","volume":"14","author":[{"given":"Yuansheng","family":"Ning","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lingfeng","family":"Sang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongbo","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luige","family":"Vladareanu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianye","family":"Niu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,10,26]]},"reference":[{"key":"77137_CR1","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1038\/s41551-022-00984-1","volume":"7","author":"C Siviy","year":"2023","unstructured":"Siviy, C. et al. Opportunities and challenges in the development of exoskeletons for locomotor assistance. Nat. Biomed. Eng. 7, 456\u2013472 (2023).","journal-title":"Nat. Biomed. Eng."},{"key":"77137_CR2","doi-asserted-by":"publisher","first-page":"2695","DOI":"10.1109\/TNSRE.2021.3136088","volume":"29","author":"M Sarajchi","year":"2021","unstructured":"Sarajchi, M., Mohamad, K. & Konstantinos, S. Wearable lower-limb exoskeleton for children with cerebral palsy: a systematic review of mechanical design, actuation type, control strategy, and clinical evaluation. IEEE Trans. Neural Syst. Rehabil Eng. 29, 2695\u20132720 (2021).","journal-title":"IEEE Trans. Neural Syst. Rehabil Eng."},{"issue":"13","key":"77137_CR3","doi-asserted-by":"publisher","first-page":"6103","DOI":"10.3390\/s23136103","volume":"23","author":"M Sarajchi","year":"2023","unstructured":"Sarajchi, M. & Konstantinos, S. Design and control of a single-leg exoskeleton with gravity compensation for children with unilateral cerebral palsy. Sensors. 23(13), 6103 (2023).","journal-title":"Sensors"},{"key":"77137_CR4","doi-asserted-by":"publisher","first-page":"e42901","DOI":"10.2196\/42901","volume":"25","author":"Y Zhang","year":"2023","unstructured":"Zhang, Y., Liu, X., Qiao, X. & Fan, Y. Characteristics and emerging trends in research on rehabilitation robots from 2001 to 2020: bibliometric study. J. Med. Internet Res. 25, e42901 (2023).","journal-title":"J. Med. Internet Res."},{"key":"77137_CR5","doi-asserted-by":"crossref","unstructured":"Mihelj, M., Nef, T. & Riener, R. ARMin II \u2013\u20097 dof rehabilitation robot: mechanics and kinematics. In 2007 International Conference on Robotics and Automation, 4120\u20134125 (IEEE, 2007).","DOI":"10.1109\/ROBOT.2007.364112"},{"key":"77137_CR6","doi-asserted-by":"crossref","unstructured":"Gopura, R. A. R. C., Kiguchi, K. & Li, Y. SUEFUL-7: a 7 dof upper-limb exoskeleton robot with muscle-model-oriented emg-based control. In 2009 IEEE\/RSJ International Conference on Intelligent Robots and Systems, 1126\u20131131 (2009).","DOI":"10.1109\/IROS.2009.5353935"},{"issue":"12","key":"77137_CR7","doi-asserted-by":"publisher","first-page":"2073","DOI":"10.1017\/S0263574719001085","volume":"37","author":"A Zeiaee","year":"2019","unstructured":"Zeiaee, A., Soltani-Zarrin, R., Langari, R. & Tafreshi, R. Kinematic design optimization of an eight degree-of-freedom upper-limb exoskeleton. Robotica. 37(12), 2073\u20132086 (2019).","journal-title":"Robotica"},{"issue":"4","key":"77137_CR8","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1177\/0278364917706743","volume":"36","author":"B Kim","year":"2017","unstructured":"Kim, B. & Deshpande, A. D. An upper-body rehabilitation exoskeleton harmony with an anatomical shoulder mechanism: design, modeling, control, and performance evaluation. Int. J. Rob. Res. 36(4), 414\u2013435 (2017).","journal-title":"Int. J. Rob. Res."},{"key":"77137_CR9","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1007\/s12206-018-0136-y","volume":"32","author":"F Xiao","year":"2018","unstructured":"Xiao, F., Gao, Y., Wang, Y., Zhu, Y. & Zhao, J. Design and evaluation of a 7-dof cable-driven upper limb exoskeleton. J. Mech. Sci. Technol. 32, 855\u2013864 (2018).","journal-title":"J. Mech. Sci. Technol."},{"issue":"3","key":"77137_CR10","doi-asserted-by":"publisher","first-page":"2131","DOI":"10.1109\/TRO.2022.3226890","volume":"39","author":"Y Zimmermann","year":"2023","unstructured":"Zimmermann, Y., Sommerhalder, P., Wolf, R., Riener, M. & Hutter Anyexo 2.0: a fully actuated upper-limb exoskeleton for manipulation and joint-oriented training in all stages of rehabilitation. IEEE Trans. Robot. 39(3), 2131\u20132150 (2023).","journal-title":"IEEE Trans. Robot"},{"key":"77137_CR11","doi-asserted-by":"publisher","first-page":"2095","DOI":"10.1007\/s12555-019-0076-7","volume":"18","author":"S Park","year":"2020","unstructured":"Park, S., Lee, M. C. & Kim, J. Trajectory planning with collision avoidance for redundant robots using Jacobian and artificial potential field-based real-time inverse kinematics. Int. J. Control Autom. Syst. 18, 2095\u20132107 (2020).","journal-title":"Int. J. Control Autom. Syst."},{"key":"77137_CR12","doi-asserted-by":"crossref","unstructured":"Huang, H., Chen, C. & Wang, P. Particle swarm optimization for solving the inverse kinematics of 7-dof robotic manipulators. In 2012 IEEE International Conference on Systems, Man, and Cybernetics, 3105\u20133110 (2012).","DOI":"10.1109\/ICSMC.2012.6378268"},{"key":"77137_CR13","doi-asserted-by":"publisher","first-page":"S20","DOI":"10.1016\/j.clinbiomech.2005.09.009","volume":"21","author":"N Klopcar","year":"2006","unstructured":"Klopcar, N. & Lenarcic, J. Bilateral and unilateral shoulder girdle kinematics during humeral elevation. Clin. Biomech. 21, S20\u2013S26 (2006).","journal-title":"Clin. Biomech."},{"key":"77137_CR14","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1142\/S0219843611002344","volume":"8","author":"W Chen","year":"2011","unstructured":"Chen, W., Xiong, C., Sun, R. & Huang, X. A 10-degree of freedom exoskeleton rehabilitation robot with ergonomic shoulder actuation mechanism. Int. J. Humanoid Rob. 8, 47\u201371 (2011).","journal-title":"Int. J. Humanoid Rob."},{"issue":"11","key":"77137_CR15","doi-asserted-by":"publisher","first-page":"3696","DOI":"10.3390\/app10113696","volume":"10","author":"J Li","year":"2020","unstructured":"Li, J., Zhang, C., Dong, M. & Cao, Q. A kinematic model of the shoulder complex obtained from a wearable detection system. Appl. Sci. 10(11), 3696 (2020).","journal-title":"Appl. Sci."},{"issue":"1","key":"77137_CR16","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/s10846-015-0212-4","volume":"80","author":"H Kim","year":"2015","unstructured":"Kim, H. & Rosen, J. Predicting redundancy of a 7 DOF upper limb exoskeleton toward improved transparency between human and robot. J. Intell. Robot Syst. 80(1), 99\u2013119 (2015).","journal-title":"J. Intell. Robot Syst."},{"issue":"3","key":"77137_CR17","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TSMC.2017.2695003","volume":"49","author":"B Brahmi","year":"2019","unstructured":"Brahmi, B., Saad, M., Rahman, M. H. & Ochoa-Luna, C. Cartesian trajectory tracking of a 7-dof exoskeleton robot based on human inverse kinematics. IEEE Trans. Syst. Man. Cybern Syst. 49(3), 600\u2013611 (2019).","journal-title":"IEEE Trans. Syst. Man. Cybern Syst."},{"issue":"S1","key":"77137_CR18","doi-asserted-by":"publisher","first-page":"123","DOI":"10.3233\/THC-199012","volume":"27","author":"G Li","year":"2019","unstructured":"Li, G. et al. Inverse kinematic analysis and trajectory planning of a modular upper limb rehabilitation exoskeleton. Technol. Health Care. 27(S1), 123\u2013132 (2019).","journal-title":"Technol. Health Care"},{"key":"77137_CR19","doi-asserted-by":"publisher","first-page":"14119","DOI":"10.1007\/s00521-021-06050-2","volume":"33","author":"S Dereli","year":"2021","unstructured":"Dereli, S. A new modified grey wolf optimization algorithm proposal for a fundamental engineering problem in robotics. Neural Comput. Applic. 33, 14119\u201314131 (2021).","journal-title":"Neural Comput. Applic"},{"issue":"3","key":"77137_CR20","doi-asserted-by":"publisher","first-page":"e2491","DOI":"10.1002\/rcs.2491","volume":"19","author":"B Niu","year":"2023","unstructured":"Niu, B. et al. Virtual-force\u2010guided intraoperative ultrasound scanning with online lesion location prediction: a phantom study. Int. J. Med. Robot. 19(3), e2491 (2023).","journal-title":"Int. J. Med. Robot"},{"key":"77137_CR21","doi-asserted-by":"publisher","first-page":"106040","DOI":"10.1016\/j.cie.2019.106040","volume":"137","author":"T Dokeroglu","year":"2019","unstructured":"Dokeroglu, T., Sevinc, E., Kucukyilmaz, T. & Cosar A. A survey on new generation metaheuristic algorithms. Comput. Ind. Eng. 137, 106040 (2019).","journal-title":"Comput. Ind. Eng."},{"issue":"2","key":"77137_CR22","first-page":"285","volume":"11","author":"S Haibin Ouyang","year":"2024","unstructured":"Haibin Ouyang, S., Liang, S., Li, Z. & Zhou Z.-H. Z. A dual population collaborative harmony search algorithm with adaptive population size for the system reliability-redundancy allocation problems. J. Comput. Des. Eng. 11(2), 285\u2013313 (2024).","journal-title":"J. Comput. Des. Eng."},{"issue":"2","key":"77137_CR23","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1016\/j.asoc.2011.11.006","volume":"12","author":"M Da Gra\u00e7a Marcos","year":"2012","unstructured":"Da Gra\u00e7a Marcos, M., Machado, J. T. & Azevedo-Perdico\u00falis, T. A multi-objective approach for the motion planning of redundant manipulators. Appl. Soft Comput. 12(2), 589\u2013599 (2012).","journal-title":"Appl. Soft Comput."},{"issue":"12","key":"77137_CR24","doi-asserted-by":"publisher","first-page":"8014","DOI":"10.1109\/TII.2021.3060019","volume":"17","author":"M Safeea","year":"2021","unstructured":"Safeea, M., Bearee, R. & Neto, P. A modified DLS scheme with controlled cyclic solution for inverse kinematics in redundant robots. IEEE Trans. Industr. Inf. 17(12), 8014\u20138023 (2021).","journal-title":"IEEE Trans. Industr. Inf."},{"key":"77137_CR25","first-page":"02619","volume":"2308","author":"V Sankar","year":"2023","unstructured":"Sankar, V. & Kumar, B. S. Bald eagle search algorithm for high precision inverse kinematics of hyper-redundant 9-dof robot. Arxiv Preprint Arxiv. 2308, 02619 (2023).","journal-title":"Arxiv Preprint Arxiv"},{"key":"77137_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10462-021-10041-z","volume":"55","author":"T Nguyen","year":"2022","unstructured":"Nguyen, T., Bui, T. & Pham, H. Using proposed optimization algorithm for solving inverse kinematics of human upper limb applying in rehabilitation robotic. Artif. Intell. Rev. 55, 1\u201327 (2022).","journal-title":"Artif. Intell. Rev."},{"key":"77137_CR27","doi-asserted-by":"publisher","first-page":"106966","DOI":"10.1016\/j.engappai.2023.106966","volume":"126","author":"D Bedolla-Martinez","year":"2023","unstructured":"Bedolla-Martinez, D., Kali, Y., Saad, M., Ochoa-Luna, C. & Rahman, M. H. Learning human inverse kinematics solutions for redundant robotic upper-limb rehabilitation. Eng. Appl. Artif. Intell. 126, 106966 (2023).","journal-title":"Eng. Appl. Artif. Intell."},{"key":"77137_CR28","doi-asserted-by":"publisher","first-page":"38","DOI":"10.3389\/fnbot.2018.00038","volume":"12","author":"K Lee","year":"2018","unstructured":"Lee, K., Park, J., Beom, J. & Park, H. Design and evaluation of passive shoulder joint tracking module for upper-limb rehabilitation robots. Front. Neurorobot. 12, 38 (2018).","journal-title":"Front. Neurorobot"},{"key":"77137_CR29","doi-asserted-by":"publisher","first-page":"5721","DOI":"10.1007\/s12206-022-1034-5","volume":"36","author":"Y Ning","year":"2022","unstructured":"Ning, Y. et al. An eight-degree-of-freedom upper extremity exoskeleton rehabilitation robot: design, optimization, and validation. J. Mech. Sci. Technol. 36, 5721\u20135733 (2022).","journal-title":"J. Mech. Sci. Technol."},{"key":"77137_CR30","doi-asserted-by":"publisher","first-page":"6199","DOI":"10.1007\/s12652-020-01815-4","volume":"11","author":"R Gao","year":"2020","unstructured":"Gao, R. Inverse kinematics solution of robotics based on neural network algorithms. J. Ambient Intell. Hum. Comput. 11, 6199\u20136209 (2020).","journal-title":"J. Ambient Intell. Hum. Comput."},{"key":"77137_CR31","first-page":"2680","volume":"01","author":"RT Marler","year":"2005","unstructured":"Marler, R. T., Rahmatalla, S., Shanahan, M. & Abdel-Malek, K. A new discomfort function for optimization-based posture prediction. SAE Tech. Paper. 01, 2680 (2005).","journal-title":"SAE Tech. Paper"},{"key":"77137_CR32","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.mechmachtheory.2014.06.015","volume":"81","author":"J Zhao","year":"2014","unstructured":"Zhao, J., Xie, B. & Song, C. Generating human-like movements for robotic arms. Mech. Mach. Theory. 81, 107\u2013128 (2014).","journal-title":"Mech. Mach. Theory"},{"issue":"5","key":"77137_CR33","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1006\/gmod.2000.0528","volume":"62","author":"D Tolani","year":"2000","unstructured":"Tolani, D., Goswami, A. & Badler, N. I. Real-time inverse kinematics techniques for anthropomorphic limbs. Graph Models. 62(5), 353\u2013388 (2000).","journal-title":"Graph Models"},{"key":"77137_CR34","doi-asserted-by":"publisher","first-page":"105190","DOI":"10.1016\/j.knosys.2019.105190","volume":"191","author":"A Faramarzi","year":"2020","unstructured":"Faramarzi, A., Heidarinejad, M., Stephens, B. & Mirjalili, S. Equilibrium optimizer: a novel optimization algorithm. Knowl. Based Syst. 191, 105190 (2020).","journal-title":"Knowl. Based Syst."},{"issue":"1","key":"77137_CR35","first-page":"012020","volume":"1682","author":"Y Wang","year":"2020","unstructured":"Wang, Y., Wang, T., Dong, S. & Yao, C. An improved grey-wolf optimization algorithm based on circle map. J. Phys. Conf. Ser. 1682(1), 012020 (2020).","journal-title":"J. Phys. : Conf. Ser."},{"key":"77137_CR36","doi-asserted-by":"crossref","unstructured":"Amoshahy, M. J., Shamsi, M. & Sedaaghi, M. H. A novel flexible inertia weight particle swarm optimization algorithm. PLoS ONE. 11(8), e0161558 (2016).","DOI":"10.1371\/journal.pone.0161558"},{"key":"77137_CR37","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/j.asoc.2014.06.034","volume":"23","author":"H Hakl\u0131","year":"2014","unstructured":"Hakl\u0131, H. & U\u011fuz, H. A novel particle swarm optimization algorithm with L\u00e9vy flight. Appl. Soft Comput. 23, 333\u2013345 (2014).","journal-title":"Appl. Soft Comput."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77137-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77137-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77137-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T07:09:10Z","timestamp":1730185750000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-77137-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,26]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["77137"],"URL":"https:\/\/doi.org\/10.1038\/s41598-024-77137-8","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,26]]},"assertion":[{"value":"6 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2024","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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"To reproduce the optimization results described above, the objective equation can be constructed by the method described in Sect.\u00a0\n                      \n                      as Eq.\u00a013. The solution using the improved EO algorithm is shown in Fig.\u00a03, and the relevant parameters are given in Table\u00a03.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Replication of results"}}],"article-number":"25476"}}