{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T12:36:02Z","timestamp":1778070962442,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2024,11,25]],"date-time":"2024-11-25T00:00:00Z","timestamp":1732492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Science and Technology Project Undertaken by Shenzhen","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}]},{"name":"National Key Science and Technology Project Undertaken by Shenzhen","award":["SQ2024162"],"award-info":[{"award-number":["SQ2024162"]}]},{"name":"National Key Science and Technology Project Undertaken by Shenzhen","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}]},{"name":"National Key Science and Technology Project Undertaken by Shenzhen","award":["202401A049"],"award-info":[{"award-number":["202401A049"]}]},{"name":"National Key Science and Technology Project Undertaken by Shenzhen","award":["LGF22E050001"],"award-info":[{"award-number":["LGF22E050001"]}]},{"name":"Hebei Province Higher Education Humanities and Social Sciences Research Project (Youth Fund Project)","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}]},{"name":"Hebei Province Higher Education Humanities and Social Sciences Research Project (Youth Fund Project)","award":["SQ2024162"],"award-info":[{"award-number":["SQ2024162"]}]},{"name":"Hebei Province Higher Education Humanities and Social Sciences Research Project (Youth Fund Project)","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}]},{"name":"Hebei Province Higher Education Humanities and Social Sciences Research Project (Youth Fund Project)","award":["202401A049"],"award-info":[{"award-number":["202401A049"]}]},{"name":"Hebei Province Higher Education Humanities and Social Sciences Research Project (Youth Fund Project)","award":["LGF22E050001"],"award-info":[{"award-number":["LGF22E050001"]}]},{"name":"Ningbo International Cooperation project","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}]},{"name":"Ningbo International Cooperation project","award":["SQ2024162"],"award-info":[{"award-number":["SQ2024162"]}]},{"name":"Ningbo International Cooperation project","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}]},{"name":"Ningbo International Cooperation project","award":["202401A049"],"award-info":[{"award-number":["202401A049"]}]},{"name":"Ningbo International Cooperation project","award":["LGF22E050001"],"award-info":[{"award-number":["LGF22E050001"]}]},{"name":"S&amp;T Program of Qinhuangdao","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}]},{"name":"S&amp;T Program of Qinhuangdao","award":["SQ2024162"],"award-info":[{"award-number":["SQ2024162"]}]},{"name":"S&amp;T Program of Qinhuangdao","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}]},{"name":"S&amp;T Program of Qinhuangdao","award":["202401A049"],"award-info":[{"award-number":["202401A049"]}]},{"name":"S&amp;T Program of Qinhuangdao","award":["LGF22E050001"],"award-info":[{"award-number":["LGF22E050001"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["CJGJZD20220517142405013"],"award-info":[{"award-number":["CJGJZD20220517142405013"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["SQ2024162"],"award-info":[{"award-number":["SQ2024162"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["2023H014"],"award-info":[{"award-number":["2023H014"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["202401A049"],"award-info":[{"award-number":["202401A049"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["LGF22E050001"],"award-info":[{"award-number":["LGF22E050001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In rehabilitation, physicians plan lower-limb exercises via linear guidance. Ensuring efficacy and safety, they design patient-specific paths, carefully plotting smooth trajectories to minimize jerks. Replicating their precision in robotics is a major challenge. This study introduces a linear rehabilitation motion planning method designed for physicians to use a multi-posture lower-limb rehabilitation robot, encompassing both path and trajectory planning. By subdividing the lower limb\u2019s action space into four distinct training sections and classifying this space, we articulate the correlation between linear trajectories and key joint rehabilitation metrics. Building upon this foundation, a rehabilitative path generation system is developed, anchored in joint rehabilitation indicators. Subsequently, high-order polynomial curves are employed to mimic the smooth continuity of traditional rehabilitation trajectories and joint motions. Furthermore, trajectory planning is refined through the resolution of a constrained quadratic optimization problem, aiming to minimize the abrupt jerks in the trajectory. The optimized trajectories derived from our experiments are compared with randomly generated trajectories, demonstrating the suitability of trajectory optimization for real-time rehabilitation trajectory planning. Additionally, we compare trajectories generated based on the two groups of joint rehabilitation indicators, indicating that the proposed path generation system effectively assists clinicians in executing efficient and precise robot-assisted rehabilitation path planning.<\/jats:p>","DOI":"10.3390\/s24237506","type":"journal-article","created":{"date-parts":[[2024,11,25]],"date-time":"2024-11-25T11:25:33Z","timestamp":1732533933000},"page":"7506","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Linear Rehabilitative Motion Planning Method with a Multi-Posture Lower-Limb Rehabilitation Robot"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8752-3669","authenticated-orcid":false,"given":"Xincheng","family":"Wang","sequence":"first","affiliation":[{"name":"Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao 066000, China"},{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Musong","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Environmental Engineering, Hebei University of Environmental Engineering, Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1029-8408","authenticated-orcid":false,"given":"Lingfeng","family":"Sang","sequence":"additional","affiliation":[{"name":"Ningbo Key Laboratory of Aging Health Equipment and Service Technology, Ningbo Polytechnic, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongbo","family":"Wang","sequence":"additional","affiliation":[{"name":"Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao 066000, China"},{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066000, China"},{"name":"Academy for Engineering & Technology, Fudan University, Shanghai 200000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfei","family":"Feng","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8040-8396","authenticated-orcid":false,"given":"Jianye","family":"Niu","sequence":"additional","affiliation":[{"name":"Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System, Yanshan University, Qinhuangdao 066000, China"},{"name":"School of Mechanical Engineering, Yanshan University, Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongfei","family":"Yu","sequence":"additional","affiliation":[{"name":"Collaborative Innovation Center for Port Industry Development in Coastal Areas, Qinhuangdao 066000, China"},{"name":"Hebei Technology Innovation Center for Intelligent Industrial Design, Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Cheng","sequence":"additional","affiliation":[{"name":"Qinhuangdao Hospital of Traditional Chinese Medicine, Qinhuangdao 066000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, W., Li, K., Yue, S., Yin, C., Yin, C., and Wei, N. (2017). Associations between lower-limb muscle activation and knee flexion in post-stroke individuals: A study on the stance-to-swing phases of gait. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0183865"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Celestino, M.L., van Emmerik, R., Barela, J.A., Bacca, O., and Barela, A.M.F. (2021). Effects of limited knee flexion movement in intra-limb gait coordination. J. Biomech., 128.","DOI":"10.1016\/j.jbiomech.2021.110712"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Li, S. (2023). Stiff knee gait disorders as neuromechanical consequences of spastic hemiplegia in chronic stroke. Toxins, 15.","DOI":"10.3390\/toxins15030204"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/j.gaitpost.2014.01.012","article-title":"The stroke-related effects of hip flexion fatigue on over ground walking","volume":"39","author":"Rybar","year":"2014","journal-title":"Gait Posture"},{"key":"ref_5","first-page":"734","article-title":"Efficacy of a hip flexion assist orthosis in adults with hemiparesis after stroke","volume":"92","author":"Carda","year":"2012","journal-title":"Phys. Ther. Rehabil. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1002\/mus.23886","article-title":"Functional implications of impaired control of submaximal hip flexion following stroke","volume":"49","author":"Hyngstrom","year":"2014","journal-title":"Muscle Nerve"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Salzmann, C., Sehle, A., and Liepert, J. (2021). Using the flexor reflex in a chronic stroke patient for gait improvement: A case report. Front. Neurol., 12.","DOI":"10.3389\/fneur.2021.691214"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0268-0033(98)00062-X","article-title":"Plantarflexor weakness as a limiting factor of gait speed in stroke subjects and the compensating role of hip flexors","volume":"14","author":"Nadeau","year":"1999","journal-title":"Clin. Biomech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1097\/NPT.0b013e31816594ea","article-title":"Lower extremity passive range of motion in community-ambulating stroke survivors","volume":"32","author":"Desimone","year":"2008","journal-title":"J. Neurol. Phys. Ther."},{"key":"ref_10","first-page":"pzab069","article-title":"Relationships between stepping-reaction movement patterns and clinical measures of balance, motor impairment, and step characteristics after stroke","volume":"101","author":"Pollock","year":"2021","journal-title":"Phys. Ther. Rehabil. J."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gomez-Cuaresma, L., Lucena-Anton, D., Gonzalez-Medina, G., Martin-Vega, F.J., Galan-Mercant, A., and Luque-Moreno, C. (2021). Effectiveness of stretching in post-stroke spasticity and range of motion: Systematic review and meta-analysis. J. Pers. Med., 11.","DOI":"10.3390\/jpm11111074"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bouri, M., Le Gall, B., and Clavel, R. (2009, January 19\u201323). A new concept of parallel robot for rehabilitation and fitness: The lambda. Proceedings of the IEEE International Conference on Robotics and Biomimetics (ROBIO), Guilin, China.","DOI":"10.1109\/ROBIO.2009.5420481"},{"key":"ref_13","unstructured":"Simon, A.M., Kelly, B.M., and Ferris, D.P. (2009, January 2\u20136). Preliminary trial of symmetry-based resistance in individuals with post-stroke hemiparesis. Proceedings of the 31st Annual International Conference of the IEEE EMBS, Minneapolis, MN, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.cmpb.2009.04.007","article-title":"Motorized CPM\/CAM physiotherapy device with sliding-mode fuzzy neural network control loop","volume":"96","author":"Ho","year":"2009","journal-title":"Comput. Meth. Programs Biomed."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sun, H., Zhang, L., Hu, X., and Tian, L. (2011, January 9\u201311). Experiment study of fuzzy impedance control on horizontal lower limbs rehabilitation robot. Proceedings of the International Conference on Electronics, Communications and Control (ICECC), Ningbo, China.","DOI":"10.1109\/ICECC.2011.6066708"},{"key":"ref_16","unstructured":"Deaconescu, T., and Deaconescu, A. (2009, January 18\u201320). Pneumatic muscle actuated isokinetic equipment for the rehabilitation of patients with disabilities of the bearing joints. Proceedings of the International Multi-Conference of Engineers and Computer Scientists (IMECS), Hong Kong."},{"key":"ref_17","unstructured":"Metrailler, P., Blanchard, V., Perrin, I., Brodard, R., Frischknecht, R., Schmitt, C., Fournier, J., Bouri, M., and Clavel, R. (2006, January 20\u201322). Improvement of rehabilitation possibilities with the MotionMaker (TM). Proceedings of the 2006 1st IEEE RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics, Pisa, Italy."},{"key":"ref_18","unstructured":"Schmitt, C., M\u00e9trailler, P., Al-Khodairy, A., Brodard, R., Fournier, J., Bouri, M., and Clavel, R. (2004, January 6\u20139). The Motion Maker\u2122: A rehabilitation system combining an orthosis with closed-loop electrical muscle stimulation. Proceedings of the 8th Vienna International Workshop on Functional Electrical Stimulation, Vienna, Austria."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/j.mechatronics.2011.01.005","article-title":"The design and control of a therapeutic exercise robot for lower limb rehabilitation: Physiotherabot","volume":"21","author":"Akdoan","year":"2011","journal-title":"Mechatronics"},{"key":"ref_20","unstructured":"Hidenori, T. (2006, January 7\u20138). Development of portable therapeutic exercise machine temlx2 influences of passive motion for lower extremities on regional cerebral blood volume. Proceedings of the Symposium on Biological and Physiological Engineering, Taipei, Taiwan."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.mechatronics.2008.07.006","article-title":"Nexos: The design, development and evaluation of a rehabilitation system for the lower limbs","volume":"19","author":"Bradley","year":"2009","journal-title":"Mechatronics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1729881418776855","DOI":"10.1177\/1729881418776855","article-title":"Mechanical design and trajectory planning of a lower limb rehabilitation robot with a variable workspace","volume":"15","author":"Wang","year":"2018","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s11370-020-00346-3","article-title":"Gait pattern generation algorithm for lower-extremity rehabilitation\u2013exoskeleton robot considering wearer\u2019s condition","volume":"14","author":"Hwang","year":"2021","journal-title":"Intell. Serv. Robot."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.rcim.2017.08.007","article-title":"Human motion intent learning based motion assistance control for a wearable exoskeleton","volume":"49","author":"Long","year":"2018","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.3390\/s140101705","article-title":"Wearable gait measurement system with an instrumented cane for exoskeleton control","volume":"14","author":"Hassan","year":"2014","journal-title":"Sensors"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"87","DOI":"10.3233\/NRE-161393","article-title":"Gait training with hybrid assistive limb enhances the gait functions in subacute stroke patients: A pilot study","volume":"40","author":"Yoshikawa","year":"2017","journal-title":"NeuroRehabilitation"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Mileti, I., Taborri, J., Torricelli, D., Rossi, S., and Patane, F. (2022, January 26\u201328). Artificial neural network for the identification of postural instability in subject wearing lower limb exoskeleton. Proceedings of the IEEE International Conference on Metrology for Extended Reality, Artificial Intelligence and Neural Engineering (IEEE MetroXRAINE), Rome, Italy.","DOI":"10.1109\/MetroXRAINE54828.2022.9967525"},{"key":"ref_28","first-page":"54","article-title":"Robot therapy with the H2 exoskeleton for gait rehabilitation in patients with incomplete spinal cord injry. A clinical experience","volume":"54","author":"Pons","year":"2020","journal-title":"Rehabilitacion"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1310\/tsr1502-131","article-title":"KineAssist: Design and development of a robotic overground gait and balance therapy device","volume":"15","author":"Patton","year":"2008","journal-title":"Top. Stroke Rehabil."},{"key":"ref_30","first-page":"43","article-title":"Patient-cooperative strategies for robot-aided treadmill training: First experimental results","volume":"7","author":"Riener","year":"2005","journal-title":"J. NeuroEng. Rehabil."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/TNSRE.2009.2033061","article-title":"Path control: A method for patient-cooperative robot-aided gait rehabilitation","volume":"18","author":"Caprez","year":"2010","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.clinbiomech.2016.04.013","article-title":"The combined effects of guidance force, bodyweight support and gait speed on muscle activity during able-bodied walking in the Lokomat","volume":"36","author":"Boonstra","year":"2016","journal-title":"Clin. Biomech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1109\/TNSRE.2007.903919","article-title":"Design and evaluation of the LOPES exoskeleton robot for interactive gait rehabilitation","volume":"15","author":"Veneman","year":"2007","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Banala, S.K., Agrawal, S.K., and Scholz, J.P. (2007, January 13\u201315). Active Leg Exoskeleton (ALEX) for Gait Rehabilitation of Motor-Impaired Patients. Proceedings of the IEEE 10th International Conference on Rehabilitation Robotics, Noordwijk, The Netherlands.","DOI":"10.1109\/ICORR.2007.4428456"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6293","DOI":"10.1177\/1687814017726293","article-title":"A wearable somatosensory teaching device with adjustable operating force for gait rehabilitation training robot","volume":"9","author":"Guo","year":"2017","journal-title":"Adv. Mech. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"62032","DOI":"10.5772\/62032","article-title":"Research and design of a new horizontal lower limb rehabilitation training robot","volume":"13","author":"Guo","year":"2016","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Lu, Y., Wang, H., Niu, J., Lu, Z., Liu, C., and Feng, N. (2025). Jump motion intention recognition and brain activity analysis based on EEG signals and Vision Transformer model. Biomed. Signal Process. Control, 100.","DOI":"10.1016\/j.bspc.2024.107001"},{"key":"ref_38","first-page":"380","article-title":"Using Fuzzy PD Controllers for Soft Motions in a Car-like Robot","volume":"3","author":"Mercorelli","year":"2018","journal-title":"Adv. Sci. Technol.-Res."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Kruse, O., Mukhamejanova, A., and Mercorelli, P. (2022). Super-Twisting Sliding Mode Control for Differential Steering Systems in Vehicular Yaw Tracking Motion. Electronics, 11.","DOI":"10.3390\/electronics11091330"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Wang, X., Wang, H., Zhang, B., Zheng, D., Yu, H., Cheng, B., and Niu, J. (2024). A Multistage Hemiplegic Lower-Limb Rehabilitation Robot: Design and Gait Trajectory Planning. Sensors, 24.","DOI":"10.3390\/s24072310"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"10852","DOI":"10.1177\/09544062221106632","article-title":"Real-time jerk-minimization trajectory planning of robotic arm based on polynomial curve optimization","volume":"236","author":"Wu","year":"2022","journal-title":"Proc. Inst. Mech. Eng. Part C-J. Eng. Mech. Eng. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/23\/7506\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:38:51Z","timestamp":1760114331000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/23\/7506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,25]]},"references-count":41,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["s24237506"],"URL":"https:\/\/doi.org\/10.3390\/s24237506","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,25]]}}}