{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T15:58:54Z","timestamp":1772553534541,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T00:00:00Z","timestamp":1693180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Major Research Plan of National Natural Science Foundation of China","award":["91648106"],"award-info":[{"award-number":["91648106"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Powered exoskeleton rehabilitation is an effective way to help stroke patients recover their motor abilities. Bionic structures and human-like control strategies can be used to enhance both the safety and efficacy of exoskeletons. However, the motion characteristics of the shoulder complex are not sufficiently considered. In this paper, we designed a 7-degrees-of-freedom (DOF) upper limb rehabilitation exoskeleton, FREE (functional rehabilitation exoskeleton). The mechanical structures of the shoulder and forearm of FREE are in accordance with human anatomy, and can be used to perform a wide range of synergistic motion of multiple joints while keeping a safe distance from the patient\u2019s head. A multiple-input-multiple-output (MIMO) shoulder girdle motion prediction model was developed to satisfy the synergy between humans and exoskeletons. Moreover, a constrained task priority and projected gradient-based inverse kinematics algorithm (CTPPG-IK) was proposed to achieve assistance with scapulohumeral rhythm. A motion capture system was used to collect different activities of daily life (ADL) motion data to validate the proposed algorithm. The experimental results show that the accuracy of the prediction model is higher than that of existing models, and the inverse kinematics algorithm can handle the end-effector task and joint space with a maximum angle error of 3.04\u00d710\u22123 rad.<\/jats:p>","DOI":"10.3390\/sym15091657","type":"journal-article","created":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T05:46:47Z","timestamp":1693201607000},"page":"1657","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Human-like Inverse Kinematics Algorithm of an Upper Limb Rehabilitation Exoskeleton"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2184-6980","authenticated-orcid":false,"given":"Shuo","family":"Pei","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Department of Naval Architecture and Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China"}]},{"given":"Jiajia","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Department of Naval Architecture and Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China"}]},{"given":"Junlong","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Department of Naval Architecture and Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China"}]},{"given":"Hesheng","family":"Yin","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Department of Naval Architecture and Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9595-4322","authenticated-orcid":false,"given":"Yufeng","family":"Yao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"},{"name":"Department of Naval Architecture and Ocean Engineering, Harbin Institute of Technology (Weihai), Weihai 264209, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.jstrokecerebrovasdis.2004.06.003","article-title":"Is stroke the most common cause of disability?","volume":"13","author":"Adamson","year":"2004","journal-title":"J. Stroke Cerebrovasc. Dis."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/S1474-4422(14)70160-7","article-title":"Constraint-induced movement therapy after stroke","volume":"14","author":"Kwakkel","year":"2015","journal-title":"Lancet Neurol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"412","DOI":"10.3389\/fneur.2019.00412","article-title":"Robot-assisted therapy in upper extremity hemiparesis: Overview of an evidence-based approach","volume":"10","author":"Duret","year":"2019","journal-title":"Front. Neurol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1012","DOI":"10.1109\/LRA.2021.3056366","article-title":"Sensor reduction, estimation, and control of an upper-limb exoskeleton","volume":"6","author":"Sun","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1109\/LRA.2021.3061361","article-title":"Inverse optimal robust adaptive controller for upper limb rehabilitation exoskeletons with inertia and load uncertainties","volume":"6","author":"Wang","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1007\/s42235-022-00283-0","article-title":"Study on Control Technology of Tendon Bionic Driving Robot System","volume":"20","author":"Xu","year":"2023","journal-title":"J. Bionic Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1155\/2009\/758631","article-title":"Isotropy of an Upper Limb Exoskeleton and the Kinematics and Dynamics of the Human Arm","volume":"6","author":"Perry","year":"2009","journal-title":"Appl. Bionics Biomech."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ergin, M.A., and Patoglu, V. (2012, January 14\u201318). ASSISTON-SE: A self-aligning shoulder-elbow exoskeleton. Proceedings of the 2012 IEEE International Conference on Robotics and Automation, St Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6225117"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7708","DOI":"10.1109\/LRA.2022.3183926","article-title":"NESM-\u03b3: An upper-limb exoskeleton with compliant actuators for clinical deployment","volume":"7","author":"Pan","year":"2022","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s42235-018-0019-7","article-title":"Mechatronic design of a synergetic upper limb exoskeletal robot and wrench-based assistive control","volume":"15","author":"He","year":"2018","journal-title":"J. Bionic Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1109\/TNSRE.2021.3107376","article-title":"Preliminary assessment of a postural synergy-based exoskeleton for post-stroke upper limb rehabilitation","volume":"29","author":"He","year":"2021","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s11370-022-00435-5","article-title":"Execution and perception of upper limb exoskeleton for stroke patients: A systematic review","volume":"15","author":"Xu","year":"2022","journal-title":"Intell. Serv. Robot."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41133-020-00043-x","article-title":"Development of robot-based upper limb devices for rehabilitation purposes: A systematic review","volume":"6","author":"Narayan","year":"2021","journal-title":"Augment. Hum. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1880","DOI":"10.1109\/LRA.2021.3138326","article-title":"CLEVERarm: A Lightweight and Compact Exoskeleton for Upper-Limb Rehabilitation","volume":"7","author":"Zeiaee","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1177\/0278364917706743","article-title":"An upper-body rehabilitation exoskeleton Harmony with an anatomical shoulder mechanism: Design, modeling, control, and performance evaluation","volume":"36","author":"Kim","year":"2017","journal-title":"Int. J. Robot. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4547","DOI":"10.1109\/LRA.2019.2935351","article-title":"Spine-inspired continuum soft exoskeleton for stoop lifting assistance","volume":"4","author":"Yang","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Burdet, E., Franklin, D.W., and Milner, T.E. (2013). Human Robotics: Neuromechanics and Motor Control, MIT Press.","DOI":"10.7551\/mitpress\/9007.001.0001"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TSMC.2017.2695003","article-title":"Cartesian trajectory tracking of a 7-DOF exoskeleton robot based on human inverse kinematics","volume":"49","author":"Brahmi","year":"2017","journal-title":"IEEE Trans. Syst. Man. Cybern. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1770","DOI":"10.1109\/TBME.2012.2194489","article-title":"Redundancy resolution of the human arm and an upper limb exoskeleton","volume":"59","author":"Kim","year":"2012","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1428","DOI":"10.1109\/TMECH.2014.2346767","article-title":"Kinematic analysis of a 5-dof upper-limb exoskeleton with a tilted and vertically translating shoulder joint","volume":"20","author":"Jung","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatronics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2684","DOI":"10.1109\/TMECH.2019.2945491","article-title":"A 5-degrees-of-freedom lightweight elbow-wrist exoskeleton for forearm fine-motion rehabilitation","volume":"24","author":"Wu","year":"2019","journal-title":"IEEE\/ASME Trans. Mechatronics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5","DOI":"10.3389\/fnbot.2018.00005","article-title":"Learning by demonstration for motion planning of upper-limb exoskeletons","volume":"12","author":"Lauretti","year":"2018","journal-title":"Front. Neurorobot."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1109\/TCYB.2018.2864784","article-title":"A learning-based hierarchical control scheme for an exoskeleton robot in human\u2013robot cooperative manipulation","volume":"50","author":"Deng","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12984-020-00680-8","article-title":"Exploiting upper-limb functional principal components for human-like motion generation of anthropomorphic robots","volume":"17","author":"Averta","year":"2020","journal-title":"J. Neuroeng. Rehabil."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1109\/TNSRE.2018.2811503","article-title":"Differential inverse kinematics of a redundant 4R exoskeleton shoulder joint","volume":"26","author":"Keemink","year":"2018","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng. A Publ. IEEE Eng. Med. Biol. Soc."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Dalla Gasperina, S., Ghonasgi, K., de Oliveira, A.C., Gandolla, M., Pedrocchi, A., and Deshpande, A. (2020, January 25\u201329). A novel inverse kinematics method for upper-limb exoskeleton under joint coordination constraints. Proceedings of the 2020 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Las Vegas, NV, USA.","DOI":"10.1109\/IROS45743.2020.9341686"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1109\/TRO.2013.2291630","article-title":"Task-space control of robot manipulators with null-space compliance","volume":"30","author":"Sadeghian","year":"2013","journal-title":"IEEE Trans. Robot."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.mechmachtheory.2017.12.005","article-title":"A novel closed-form solution for the inverse kinematics of redundant manipulators through workspace analysis","volume":"121","author":"Zaplana","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_29","first-page":"1703","article-title":"Riemannian optimization for distance-geometric inverse kinematics","volume":"38","author":"Giamou","year":"2021","journal-title":"IEEE Trans. Robot."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"103843","DOI":"10.1016\/j.robot.2021.103843","article-title":"Towards autonomous ergonomic upper-limb exoskeletons: A computational approach for planning a human-like path","volume":"145","author":"Zarrin","year":"2021","journal-title":"Robot. Auton. Syst."},{"key":"ref_31","unstructured":"Jackson, P., and Newmann, D. (2009). Essentials of Kinesiology for the Physical Therapist Assistant, Elsevier Health Sciences."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1007\/s11517-007-0226-6","article-title":"ARMin: A robot for patient-cooperative arm therapy","volume":"45","author":"Nef","year":"2007","journal-title":"Med Biol. Eng. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"S20","DOI":"10.1016\/j.clinbiomech.2005.09.009","article-title":"Bilateral and unilateral shoulder girdle kinematics during humeral elevation","volume":"21","year":"2006","journal-title":"Clin. Biomech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1016\/j.patrec.2013.01.015","article-title":"Multi-output least-squares support vector regression machines","volume":"34","author":"Xu","year":"2013","journal-title":"Pattern Recognit. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1115\/1.3143764","article-title":"Inverse kinematic solutions with singularity robustness for robot manipulator control","volume":"108","author":"Nakamura","year":"1986","journal-title":"J. Dyn. Syst. Meas. Control"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1109\/TSMC.1977.4309644","article-title":"Automatic supervisory control of the configuration and behavior of multibody mechanisms","volume":"7","author":"Liegeois","year":"1977","journal-title":"IEEE Trans. Syst. Man. Cybern."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498700600201","article-title":"Task-priority based redundancy control of robot manipulators","volume":"6","author":"Nakamura","year":"1987","journal-title":"Int. J. Robot. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1016\/j.jbiomech.2004.05.042","article-title":"ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion Part II: Shoulder, elbow, wrist and hand","volume":"38","author":"Wu","year":"2005","journal-title":"J. Biomech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1007\/s12206-008-0427-4","article-title":"Damped least square based genetic algorithm with Ggaussian distribution of damping factor for singularity-robust inverse kinematics","volume":"22","author":"Phuoc","year":"2008","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Tang, W., and Zhang, J. (2008, January 20\u201322). Algorithm for multi-joint redundant robot inverse kinematics based on the bayesian-BP neural network. Proceedings of the 2008 International Conference on Intelligent Computation Technology and Automation (ICICTA), Changsha, China.","DOI":"10.1109\/ICICTA.2008.406"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"791796","DOI":"10.3389\/fnbot.2022.791796","article-title":"Inverse kinematics solution of 6-DOF manipulator based on multi-objective full-parameter optimization PSO algorithm","volume":"16","author":"Luo","year":"2022","journal-title":"Front. Neurorobot."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.robot.2005.09.011","article-title":"Inverse kinematics and geometrically bounded singularities prevention of redundant manipulators: An Artificial Neural Network approach","volume":"53","author":"Mayorga","year":"2005","journal-title":"Robot. Auton. Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1657\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:40:55Z","timestamp":1760128855000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/9\/1657"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,28]]},"references-count":42,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["sym15091657"],"URL":"https:\/\/doi.org\/10.3390\/sym15091657","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,28]]}}}