{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T18:36:49Z","timestamp":1789670209777,"version":"4.0.1"},"reference-count":53,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:00:00Z","timestamp":1737504000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000150","name":"Division of Emerging Frontiers in Research and Innovation","doi-asserted-by":"publisher","award":["NFRFE2018-01698"],"award-info":[{"award-number":["NFRFE2018-01698"]}],"id":[{"id":"10.13039\/100000150","id-type":"DOI","asserted-by":"publisher"}]},{"name":"New Frontiers in Research Fund","award":["NFRFE2022-620"],"award-info":[{"award-number":["NFRFE2022-620"]}]},{"name":"NSERC Discovery","award":["RGPIN-2018-04850"],"award-info":[{"award-number":["RGPIN-2018-04850"]}]},{"name":"John R. Evans Leaders Fund Canadian Foundation for Innovation"},{"DOI":"10.13039\/100012171","name":"Ontario Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100012171","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NSERC CGS-M"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>\n                    Lower-limb exoskeletons have demonstrated great potential for gait rehabilitation in individuals with motor impairments; however, maintaining human-exoskeleton coordination remains a challenge. The coordination problem, referred to as any mismatch or asynchrony between the user\u2019s intended trajectories and exoskeleton desired trajectories, leads to sub-optimal gait performance, particularly for individuals with residual motor ability. Here, we investigate the virtual energy regulator (VER)\u2019s ability to generate coordinated locomotion in lower limb exoskeleton.\n                    <jats:italic>Contribution:<\/jats:italic>\n                    (1) In this paper, we experimented VER on a group of nine healthy individuals at different speeds (0.6\n                    <jats:italic>m<\/jats:italic>\n                    \/\n                    <jats:italic>s<\/jats:italic>\n                    \u2212 0.85\n                    <jats:italic>m<\/jats:italic>\n                    \/\n                    <jats:italic>s<\/jats:italic>\n                    ) to study the resultant gait coordination and naturalness on a large group of users. (2) The resultant assisted gait is compared to the natural and passive (zero-torque exoskeleton) walking conditions in terms of muscle activities, kinematic, spatiotemporal and kinetic measures, and questionnaires. (3) Moreover, we presented the VER\u2019s convergence proof considering the user contribution to the gait and introduced a metric to measure the user\u2019s contribution to gait. (4) We also compared VER performance with the phase-based path controller in terms of muscle effort reduction and joint kinematics using three able-bodied individuals.\n                    <jats:italic>Results:<\/jats:italic>\n                    (1) The results from the VER demonstrate the emergence of natural, coordinated locomotion, resulting in an average muscle effort reduction ranging from 13.1% to 17.7% at different speeds compared to passive walking. (2) The results from VER revealed improvements in all indicators towards natural gait when compared to walking with a zero-torque exoskeleton, for instance, an enhancement in average knee extension ranging from 3.9 to 4.1 degrees. All indicators suggest that the VER preserves natural gait variability and user engagement in locomotion control. (3) Using VER also yields in 13.9%, 15.1%, and 7.0% average muscle effort reduction when compared to the phase-based path controller. (4) Finally, using our proposed metric, we demonstrated that the resultant locomotion limit cycle is a linear combination of human-intended limit cycle and the VER\u2019s limit cycle. These findings may have implications for understanding how the central nervous system controls our locomotion.\n                  <\/jats:p>","DOI":"10.1371\/journal.pone.0292334","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T13:23:47Z","timestamp":1737552227000},"page":"e0292334","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":9,"title":["Coordinated human-exoskeleton locomotion emerges from regulating virtual energy"],"prefix":"10.1371","volume":"20","author":[{"given":"Rezvan","family":"Nasiri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hannah","family":"Dinovitzer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nirosh","family":"Manohara","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7609-6553","authenticated-orcid":true,"given":"Arash","family":"Arami","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"issue":"1","key":"pone.0292334.ref001","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1177\/0278364919853618","article-title":"Design of physical user\u2013robot interactions for model identification of soft actuators on exoskeleton robots","volume":"40","author":"M Hamaya","year":"2021","journal-title":"The International Journal of Robotics Research"},{"issue":"6","key":"pone.0292334.ref002","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1097\/WCO.0000000000000025","article-title":"The interaction between training and plasticity in the post-stroke brain","volume":"26","author":"SR Zeiler","year":"2013","journal-title":"Current Opinion in Neurology"},{"key":"pone.0292334.ref003","doi-asserted-by":"crossref","first-page":"e73","DOI":"10.1016\/j.wneu.2017.10.080","article-title":"Hybrid assistive limb exoskeleton HAL in the rehabilitation of chronic spinal cord injury: proof of concept; the results in 21 patients","volume":"110","author":"O Jansen","year":"2018","journal-title":"World neurosurgery"},{"issue":"7555","key":"pone.0292334.ref004","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1038\/nature14288","article-title":"Reducing the energy cost of human walking using an unpowered exoskeleton","volume":"522","author":"SH Collins","year":"2015","journal-title":"Nature"},{"issue":"10","key":"pone.0292334.ref005","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.1109\/TNSRE.2018.2872889","article-title":"Reducing the energy cost of human running using an unpowered exoskeleton","volume":"26","author":"R Nasiri","year":"2018","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"4-5","key":"pone.0292334.ref006","doi-asserted-by":"crossref","first-page":"722","DOI":"10.1177\/0278364920961452","article-title":"A hip\u2013knee\u2013ankle exoskeleton emulator for studying gait assistance","volume":"40","author":"GM Bryan","year":"2021","journal-title":"The International Journal of Robotics Research"},{"key":"pone.0292334.ref007","doi-asserted-by":"crossref","unstructured":"Witte KA, Zhang J, Jackson RW, Collins SH. Design of two lightweight, high-bandwidth torque-controlled ankle exoskeletons. In: 2015 IEEE International Conference on Robotics and Automation (ICRA). IEEE; 2015. p. 1223\u20131228.","DOI":"10.1109\/ICRA.2015.7139347"},{"issue":"2","key":"pone.0292334.ref008","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1109\/LRA.2021.3136240","article-title":"Underactuated soft hip exosuit based on adaptive oscillators to assist human locomotion","volume":"7","author":"E Tricomi","year":"2021","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"6","key":"pone.0292334.ref009","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1038\/s42256-022-00495-3","article-title":"A textile exomuscle that assists the shoulder during functional movements for everyday life","volume":"4","author":"AM Georgarakis","year":"2022","journal-title":"Nature Machine Intelligence"},{"key":"pone.0292334.ref010","doi-asserted-by":"crossref","unstructured":"Wehner M, Quinlivan B, Aubin PM, Martinez-Villalpando E, Baumann M, Stirling L, et al. A lightweight soft exosuit for gait assistance. In: 2013 IEEE international conference on robotics and automation. IEEE; 2013. p. 3362\u20133369.","DOI":"10.1109\/ICRA.2013.6631046"},{"issue":"2","key":"pone.0292334.ref011","doi-asserted-by":"crossref","first-page":"eaah4416","DOI":"10.1126\/scirobotics.aah4416","article-title":"Assistance magnitude versus metabolic cost reductions for a tethered multiarticular soft exosuit","volume":"2","author":"BT Quinlivan","year":"2017","journal-title":"Science robotics"},{"issue":"15","key":"pone.0292334.ref012","doi-asserted-by":"crossref","first-page":"eaar5438","DOI":"10.1126\/scirobotics.aar5438","article-title":"Human-in-the-loop optimization of hip assistance with a soft exosuit during walking","volume":"3","author":"Y Ding","year":"2018","journal-title":"Science robotics"},{"key":"pone.0292334.ref013","unstructured":"Center NSCIS, et al. Spinal Cord Injury Facts and Figures at a Glance. 2019 SCI Data Sheet. Online) https:\/\/wwwnsciscuabedu\/Public\/Facts. 2020;."},{"issue":"3","key":"pone.0292334.ref014","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1002\/pri.222","article-title":"The recovery of walking ability and subclassification of stroke","volume":"6","author":"G Baer","year":"2001","journal-title":"Physiotherapy Research International"},{"issue":"11","key":"pone.0292334.ref015","doi-asserted-by":"crossref","first-page":"1466","DOI":"10.2522\/ptj.20050266","article-title":"Metabolic costs and muscle activity patterns during robotic-and therapist-assisted treadmill walking in individuals with incomplete spinal cord injury","volume":"86","author":"JF Israel","year":"2006","journal-title":"Physical therapy"},{"key":"pone.0292334.ref016","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.jot.2015.09.007","article-title":"Recent developments and challenges of lower extremity exoskeletons","volume":"5","author":"B Chen","year":"2016","journal-title":"Journal of Orthopaedic Translation"},{"issue":"1","key":"pone.0292334.ref017","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1109\/LRA.2023.3331674","article-title":"Feedforward Control of Lower Limb Exoskeletons: Which Torque Profile Should We Use?","volume":"9","author":"H Dinovitzer","year":"2023","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"3","key":"pone.0292334.ref018","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1109\/TNSRE.2008.918389","article-title":"Optimizing compliant, model-based robotic assistance to promote neurorehabilitation","volume":"16","author":"ET Wolbrecht","year":"2008","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"1","key":"pone.0292334.ref019","first-page":"1","article-title":"Online Reference Trajectory Adaptation: A Personalized Control Strategy for Lower Limb Exoskeletons","volume":"1","author":"M Shushtari","year":"2021","journal-title":"IEEE Robotics and Automation Letters"},{"key":"pone.0292334.ref020","article-title":"Autonomous Locomotion Trajectory Shaping and Nonlinear Control for Lower Limb Exoskeletons","author":"M Sharifi","year":"2022","journal-title":"IEEE\/ASME Transactions on Mechatronics"},{"issue":"4","key":"pone.0292334.ref021","doi-asserted-by":"crossref","first-page":"1566","DOI":"10.1109\/TASE.2018.2886376","article-title":"Learning physical human\u2013robot interaction with coupled cooperative primitives for a lower exoskeleton","volume":"16","author":"R Huang","year":"2019","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"1","key":"pone.0292334.ref022","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":"A Duschau-Wicke","year":"2009","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"6","key":"pone.0292334.ref023","doi-asserted-by":"crossref","first-page":"956","DOI":"10.1109\/TNSRE.2014.2360822","article-title":"Assist-as-needed robot-aided gait training improves walking function in individuals following stroke","volume":"23","author":"S Srivastava","year":"2014","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"1","key":"pone.0292334.ref024","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1109\/TRO.2017.2768035","article-title":"A controller for guiding leg movement during overground walking with a lower limb exoskeleton","volume":"34","author":"A Martinez","year":"2017","journal-title":"IEEE Transactions on Robotics"},{"issue":"2","key":"pone.0292334.ref025","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1109\/TRO.2018.2883819","article-title":"A velocity-field-based controller for assisting leg movement during walking with a bilateral hip and knee lower limb exoskeleton","volume":"35","author":"A Martinez","year":"2018","journal-title":"IEEE Transactions on Robotics"},{"key":"pone.0292334.ref026","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez A, Lawson B, Goldfarb M. A velocity-based flow field control approach for reshaping movement of stroke-impaired individuals with a lower-limb exoskeleton. In: 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC). IEEE; 2018. p. 2797\u20132800.","DOI":"10.1109\/EMBC.2018.8512807"},{"issue":"3","key":"pone.0292334.ref027","doi-asserted-by":"crossref","first-page":"7014","DOI":"10.1109\/LRA.2022.3179420","article-title":"Reinforcement learning impedance control of a robotic prosthesis to coordinate with human intact knee motion","volume":"7","author":"R Wu","year":"2022","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"4","key":"pone.0292334.ref028","doi-asserted-by":"crossref","first-page":"11126","DOI":"10.1109\/LRA.2022.3196105","article-title":"Imposing Healthy Hip Motion Pattern and Range by Exoskeleton Control for Individualized Assistance","volume":"7","author":"Q Zhang","year":"2022","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"1","key":"pone.0292334.ref029","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1109\/TCST.2016.2646319","article-title":"Underactuated potential energy shaping with contact constraints: Application to a powered knee-ankle orthosis","volume":"26","author":"G Lv","year":"2017","journal-title":"IEEE Transactions on Control Systems Technology"},{"key":"pone.0292334.ref030","doi-asserted-by":"crossref","first-page":"95427","DOI":"10.1109\/ACCESS.2021.3094979","article-title":"Trajectory-free control of lower-limb exoskeletons through underactuated total energy shaping","volume":"9","author":"G Lv","year":"2021","journal-title":"IEEE Access"},{"issue":"2","key":"pone.0292334.ref031","doi-asserted-by":"crossref","first-page":"3273","DOI":"10.1109\/LRA.2022.3144519","article-title":"Human-in-the-Loop Weight Compensation in Upper Limb Wearable Robots Towards Total Muscles\u2019 Effort Minimization","volume":"7","author":"R Nasiri","year":"2022","journal-title":"IEEE Robotics and Automation Letters"},{"issue":"12","key":"pone.0292334.ref032","doi-asserted-by":"crossref","first-page":"2636","DOI":"10.1016\/j.jbiomech.2006.12.006","article-title":"Learning to walk with a robotic ankle exoskeleton","volume":"40","author":"KE Gordon","year":"2007","journal-title":"Journal of biomechanics"},{"issue":"1","key":"pone.0292334.ref033","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s12984-015-0086-5","article-title":"Learning to walk with an adaptive gain proportional myoelectric controller for a robotic ankle exoskeleton","volume":"12","author":"JR Koller","year":"2015","journal-title":"Journal of neuroengineering and rehabilitation"},{"issue":"2","key":"pone.0292334.ref034","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1046\/j.1525-1403.2003.03019.x","article-title":"FES gait re-education: The swing phase estimation","volume":"6","author":"I Cikajlo","year":"2003","journal-title":"Neuromodulation: Technology at the Neural Interface"},{"issue":"5","key":"pone.0292334.ref035","doi-asserted-by":"crossref","first-page":"425","DOI":"10.3233\/THC-2002-10506","article-title":"Swing phase estimation in paralyzed persons walking","volume":"10","author":"I Cikajlo","year":"2002","journal-title":"Technology and Health Care"},{"issue":"1","key":"pone.0292334.ref036","doi-asserted-by":"crossref","first-page":"66","DOI":"10.3390\/s16010066","article-title":"Gait partitioning methods: A systematic review","volume":"16","author":"J Taborri","year":"2016","journal-title":"Sensors"},{"issue":"3","key":"pone.0292334.ref037","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1109\/TRO.2018.2794536","article-title":"Continuous-phase control of a powered knee\u2013ankle prosthesis: Amputee experiments across speeds and inclines","volume":"34","author":"D Quintero","year":"2018","journal-title":"IEEE Transactions on Robotics"},{"issue":"2","key":"pone.0292334.ref038","doi-asserted-by":"crossref","first-page":"3491","DOI":"10.1109\/LRA.2021.3062562","article-title":"Real-time gait phase estimation for robotic hip exoskeleton control during multimodal locomotion","volume":"6","author":"I Kang","year":"2021","journal-title":"IEEE Robotics and Automation Letters"},{"key":"pone.0292334.ref039","doi-asserted-by":"crossref","DOI":"10.1017\/wtc.2020.11","article-title":"Real-time gait metric estimation for everyday gait training with wearable devices in people poststroke","volume":"2","author":"P Arens","year":"2021","journal-title":"Wearable technologies"},{"key":"pone.0292334.ref040","doi-asserted-by":"crossref","first-page":"2793","DOI":"10.1109\/TNSRE.2022.3207919","article-title":"Ultra-Robust Real-Time Estimation of Gait Phase","volume":"30","author":"M Shushtari","year":"2022","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"4","key":"pone.0292334.ref041","doi-asserted-by":"crossref","first-page":"7699","DOI":"10.1109\/LRA.2021.3098243","article-title":"Virtual Energy Regulator: A Time-Independent Solution for Control of Lower Limb Exoskeletons","volume":"6","author":"R Nasiri","year":"2021","journal-title":"IEEE Robotics and Automation Letters"},{"key":"pone.0292334.ref042","doi-asserted-by":"crossref","unstructured":"Nasiri R, Dinovitzer H, Arami A. A Unified Gait Phase Estimation and Control of Exoskeleton using Virtual Energy Regulator (VER). In: 2022 International Conference on Rehabilitation Robotics (ICORR). IEEE; 2022. p. 1\u20136.","DOI":"10.1109\/ICORR55369.2022.9896572"},{"key":"pone.0292334.ref043","volume-title":"Nonlinear systems","author":"HK Khalil","year":"2002"},{"key":"pone.0292334.ref044","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/B978-0-12-814659-0.00011-4","article-title":"Lower limb exoskeleton systems\u2014overview","author":"H Lee","year":"2020","journal-title":"Wearable Robotics"},{"key":"pone.0292334.ref045","doi-asserted-by":"crossref","unstructured":"Lee H, Krebs HI, Hogan N. A novel characterization method to study multivariable joint mechanical impedance. In: 2012 4th IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob). IEEE; 2012. p. 1524\u20131529.","DOI":"10.1109\/BioRob.2012.6290301"},{"key":"pone.0292334.ref046","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JTEHM.2016.2601613","article-title":"Summary of human ankle mechanical impedance during walking","volume":"4","author":"H Lee","year":"2016","journal-title":"IEEE journal of translational engineering in health and medicine"},{"issue":"4","key":"pone.0292334.ref047","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1152\/jn.00989.2014","article-title":"Modeling and simulating the neuromuscular mechanisms regulating ankle and knee joint stiffness during human locomotion","volume":"114","author":"M Sartori","year":"2015","journal-title":"Journal of neurophysiology"},{"issue":"8","key":"pone.0292334.ref048","doi-asserted-by":"crossref","first-page":"1808","DOI":"10.1109\/TNSRE.2020.3005389","article-title":"A clustering-based approach to identify joint impedance during walking","volume":"28","author":"A Arami","year":"2020","journal-title":"IEEE Transactions on Neural Systems and Rehabilitation Engineering"},{"issue":"1","key":"pone.0292334.ref049","doi-asserted-by":"crossref","first-page":"8189","DOI":"10.1038\/s41598-022-11102-1","article-title":"A neuromuscular model of human locomotion combines spinal reflex circuits with voluntary movements","volume":"12","author":"R Ramadan","year":"2022","journal-title":"Scientific Reports"},{"issue":"1","key":"pone.0292334.ref050","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1038\/s41598-018-37460-3","article-title":"Neuromusculoskeletal model that walks and runs across a speed range with a few motor control parameter changes based on the muscle synergy hypothesis","volume":"9","author":"S Aoi","year":"2019","journal-title":"Scientific reports"},{"key":"pone.0292334.ref051","article-title":"Human Gait Cost Function Varies with Walking Speed: an Inverse Optimal Control Study","author":"J Weng","year":"2023","journal-title":"IEEE Robotics and Automation Letters"},{"key":"pone.0292334.ref052","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.gaitpost.2017.10.024","article-title":"Moving from laboratory to real life conditions: Influence on the assessment of variability and stability of gait","volume":"59","author":"P Tamburini","year":"2018","journal-title":"Gait & posture"},{"issue":"3","key":"pone.0292334.ref053","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s002210050738","article-title":"The uncontrolled manifold concept: identifying control variables for a functional task","volume":"126","author":"JP Scholz","year":"1999","journal-title":"Experimental brain research"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0292334","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T13:24:17Z","timestamp":1737552257000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0292334"}},"subtitle":[],"editor":[{"given":"Imre","family":"Cikajlo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2025,1,22]]},"references-count":53,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1,22]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0292334","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2023.09.20.558567","asserted-by":"object"}]},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,22]]}}}