{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:41:19Z","timestamp":1760146879385,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T00:00:00Z","timestamp":1735603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>An ankle sprain can be caused by daily activities such as running, walking, or playing sports. In many cases, the patient\u2019s ankle suffers severe or permanent damage that requires rehabilitation to return to its initial state. Thanks to technological advances, robotics has allowed for the development of machines that generate precise, efficient, and safe movements. In addition, these machines are manipulated by a specific control depending on the rehabilitation objective. Impedance control is used in ankle rehabilitation machines for active\u2013resistive-type rehabilitation, where the patient participates by exerting a force on the machine repeatedly. Serious games are an example of an activity where the patient can interact with a video game while rehabilitating. Currently, most machines involving impedance control and targeted at serious gaming applications are mechanically composed of one degree of freedom, so the addition of another degree is a novelty. This paper presents simulation results comparing different impedance controls reported in the literature to determine the best option for applying a 2-DOF ankle rehabilitation machine using serious games. The results obtained are presented by comparing them according to the force applied to the rehabilitation machine (emulating the behavior of a patient). From the impedance controllers analyzed for horizontal (abduction\/adduction) and vertical (dorsiflexion\/plantarflexion) movements in the rehabilitation machine, it was determined that the PD control, which considers some mechanical parameters, presents a better performance. With this controller, fast and smooth angular movements are generated, while the consumption of kinetic energy is kept in a low range, proportional to the applied forces, compared to the other impedance controls analyzed.<\/jats:p>","DOI":"10.3390\/computation13010007","type":"journal-article","created":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T13:37:51Z","timestamp":1735738671000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Impedance Controller Analysis for a Two-Degrees-Of-Freedom Ankle Rehabilitation Machine with Serious Game Interactions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5108-6268","authenticated-orcid":false,"given":"Oscar I.","family":"Cirilo-Pi\u00f1on","sequence":"first","affiliation":[{"name":"TecNM\/Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Cuernavaca 62490, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4547-3739","authenticated-orcid":false,"given":"Agust\u00edn","family":"Barrera-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"TecNM\/Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Cuernavaca 62490, Mexico"}]},{"given":"Cesar H.","family":"Guzm\u00e1n-Valdivia","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mecatr\u00f3nica, Universidad Polit\u00e9cnica de Aguascalientes, Aguascalientes 20342, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8106-3673","authenticated-orcid":false,"given":"Manuel","family":"Adam-Medina","sequence":"additional","affiliation":[{"name":"TecNM\/Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Cuernavaca 62490, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3380-2598","authenticated-orcid":false,"given":"Rafael","family":"Campos-Amezcua","sequence":"additional","affiliation":[{"name":"TecNM\/Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Cuernavaca 62490, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0088-6863","authenticated-orcid":false,"given":"Andr\u00e9s","family":"Blanco-Ortega","sequence":"additional","affiliation":[{"name":"TecNM\/Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Cuernavaca 62490, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5288-079X","authenticated-orcid":false,"given":"Arturo","family":"Mart\u00ednez-Mata","sequence":"additional","affiliation":[{"name":"TecNM\/Centro Nacional de Investigaci\u00f3n y Desarrollo Tecnol\u00f3gico, Cuernavaca 62490, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1080\/17483107.2019.1578424","article-title":"Robot-assisted ankle rehabilitation: A review","volume":"15","year":"2020","journal-title":"Disabil. Rehabil. Assist. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.csm.2009.09.006","article-title":"Rehabilitation of Ankle and Foot Injuries in Athletes","volume":"29","author":"Chinn","year":"2010","journal-title":"Clin. Sports Med."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1249\/JSR.0000000000000603","article-title":"Ankle Sprains: Evaluation, Rehabilitation, and Prevention","volume":"18","author":"Chen","year":"2019","journal-title":"Curr. Sports Med. Rep."},{"key":"ref_4","first-page":"45","article-title":"Major Trends in the Development of Ankle Rehabilitation Devices","volume":"176","author":"Alcocer","year":"2012","journal-title":"Dyna"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"96","DOI":"10.21595\/vp.2022.22507","article-title":"Robot device for ankle joint rehabilitation: A review","volume":"41","author":"Zhetenbayev","year":"2022","journal-title":"Vibroeng. Procedia"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pasqual, T.B., Caurin, G.A.P., and Siqueira, A.A.G. (2016, January 26\u201329). Serious game development for Ankle rehabilitation aiming at user experience. Proceedings of the IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics, Singapore.","DOI":"10.1109\/BIOROB.2016.7523762"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Salazar, A.M., Ortega, A.B., Velasco, K.G., and Pliego, A.A. (2018). Mechatronic integral ankle rehabilitation system: Ankle rehabilitation robot, serious game, and facial expression recognition system. Advanced Topics on Computer Vision, Control and Robotics in Mechatronics, Springer.","DOI":"10.1007\/978-3-319-77770-2_11"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhang, C., Hu, J., Ai, Q., Meng, W., and Liu, Q. (2017). Impedance control of a pneumatic muscles-driven ankle rehabilitation robot. Lecture Notes in Computer Science, Springer Verlag.","DOI":"10.1007\/978-3-319-65289-4_29"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ortega, A.B., Salazar, A.M., Valdivia, C.H.G., Becerra, F.A.G., Gallegos, M.J.P., Velarde, M.A.G., and Camilo, J.A.S. (2022). CNC Machines for Rehabilitation: Ankle and Shoulder. Machines, 10.","DOI":"10.3390\/machines10111055"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"de O Andrade, K., Fernandes, G., Martins, J., Roma, V.C., Joaquim, R.C., and Caurin, G.A.P. (2013, January 18\u201320). Rehabilitation robotics and serious games: An initial architecture for simultaneous players. Proceedings of the ISSNIP Biosignals and Biorobotics Conference, BRC, Rio de Janeiro, Brazil.","DOI":"10.1109\/BRC.2013.6487455"},{"key":"ref_11","first-page":"255","article-title":"Dise\u00f1o y control de un sistema interactivo para la rehabilitaci\u00f3n de tobillo: TobiBot","volume":"5","author":"Carrera","year":"2014","journal-title":"Ing. Mec\u00e1nica. Tecnol. Desarro."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Alves, T., Gon\u00e7alves, R.S., and Carbone, G. (2022). Serious Games Strategies With Cable-Driven Robots for Bimanual Rehabilitation: A Randomized Controlled Trial with Post-Stroke Patients. Front. Robot. AI, 9.","DOI":"10.3389\/frobt.2022.739088"},{"key":"ref_13","first-page":"33","article-title":"Development of AnkleReHabit\u2014A Low-Cost Robot-Aided Ankle Rehabilitation Platform","volume":"18","author":"Tran","year":"2023","journal-title":"J. Tech. Educ. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1109\/TNSRE.2021.3104091","article-title":"Impedance Control of Human Ankle Joint With Electrically Stimulated Antagonistic Muscle Co-Contraction","volume":"29","author":"Kim","year":"2021","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1109\/TLA.2017.7910190","article-title":"Active Rehabilitation Exercises With a Parallel Structure Ankle Rehabilitation Prototype","volume":"15","author":"Rosado","year":"2017","journal-title":"IEEE Lat. Am. Trans."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1682\/JRRD.2010.04.0078","article-title":"Short-term ankle motor performance with ankle robotics training in chronic hemiparetic stroke","volume":"48","author":"Roy","year":"2011","journal-title":"J. Rehabil. Res. Dev."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gon\u00e7alves, A.C.B.F., Santos, W.M.D., Consoni, L.J., and Siqueira, A.A.G. (2014, January 14\u201316). Serious games for assessment and rehabilitation of ankle movements. Proceedings of the SeGAH 2014\u2014IEEE 3rd International Conference on Serious Games and Applications for Health, Books of Proceedings, Rio de Janeiro, Brazil.","DOI":"10.1109\/SeGAH.2014.7067071"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Perez-Ibarra, J.C., Siqueira, A.A.G., and Krebs, H.I. (2015, January 11\u201314). Assist-As-needed ankle rehabilitation based on adaptive impedance control. Proceedings of the IEEE International Conference on Rehabilitation Robotics, Singapore.","DOI":"10.1109\/ICORR.2015.7281287"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gobron, S.C., Zannini, N., Wenk, N., Schmitt, C., Charrotton, Y., Fauquex, A., Lauria, M., Degache, F., and Frischknecht, R. (2015). Serious games for rehabilitation using Head-Mounted display and haptic devices. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer.","DOI":"10.1007\/978-3-319-22888-4_15"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1109\/TNSRE.2016.2584003","article-title":"Developing a Wearable Ankle Rehabilitation Robotic Device for in-Bed Acute Stroke Rehabilitation","volume":"25","author":"Ren","year":"2017","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/16878140211004034","article-title":"A hybrid control strategy for grinding and polishing robot based on adaptive impedance control","volume":"13","author":"Zhou","year":"2021","journal-title":"Adv. Mech. Eng."},{"key":"ref_22","first-page":"162","article-title":"Review on Serious Games for Ankle Rehabilitation","volume":"7","author":"Ortega","year":"2024","journal-title":"Tecnol. Cienc. Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/978-3-030-69547-7_75","article-title":"Visual Feedback Strategy Based on Serious Games for Therapy with T-FLEX Ankle Exoskeleton","volume":"27","author":"Pino","year":"2022","journal-title":"Biosyst. Biorobot."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Covaciu, F., Pisla, A., and Iordan, A.E. (2021). Development of a virtual reality simulator for an intelligent robotic system used in ankle rehabilitation. Sensors, 21.","DOI":"10.3390\/s21041537"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"58","DOI":"10.5753\/jis.2021.1916","article-title":"Development and Test of a Serious Game for Dorsiflexion and Plantarflexion Exercises of the Feet","volume":"12","author":"Ferreira","year":"2021","journal-title":"J. Interact. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Pino, A., Gomez-Vargas, D., Garzon, A., Roberti, F., Carelli, R., Munera, M., and Cifuentes, C.A. (2022, January 25\u201329). Mirror-Based Robotic Therapy for Ankle Recovery with a Serious Game: A Case Study with a Neurological Patient. Proceedings of the IEEE International Conference on Rehabilitation Robotics, Rotterdam, The Netherlands.","DOI":"10.1109\/ICORR55369.2022.9896510"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Galli, J., Baranyi, R., Hoelbling, D., Pinter, K., Aigner, C., H\u00f6rner, W., and Grechenig, T. (2023). Prevention and Rehabilitation Gaming Support for Ankle Injuries Usable by Semi-Professional Athletes Using Commercial Off-the-Shelf Sensors. Appl. Sci., 13.","DOI":"10.3390\/app13169193"},{"key":"ref_28","first-page":"100","article-title":"Design and control of a parallel robot for ankle rehabilitation","volume":"8","author":"Tsoi","year":"2010","journal-title":"Int. J. Intell. Syst. Technol. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1109\/TRO.2009.2019783","article-title":"Robot-Aided Neurorehabilitation: A Novel Robot for Ankle Rehabilitation","volume":"25","author":"Roy","year":"2009","journal-title":"IEEE Trans. Robot."},{"key":"ref_30","unstructured":"Ortega, A.B., Rivera, H.R.A., Vald\u00e9s, L.G.V., and Bautista, R.F.V. (2013, January 13\u201315). M\u00e1quina de Rehabilitaci\u00f3n de Tobillo: Prototipo virtual y f\u00edsico. Proceedings of the X Congreso Internacional sobre Innovaci\u00f3n y Desarrollo Tecnol\u00f3gico CIINDET 2013, Cuernavaca Morelos, Mexico."},{"key":"ref_31","first-page":"e359","article-title":"Dise\u00f1o, construcci\u00f3n y control de un novedoso dispositivo de rehabilitaci\u00f3n de tobillo","volume":"7","year":"2024","journal-title":"Rev. Cienc. Tecnol."},{"key":"ref_32","first-page":"221","article-title":"Ankle injuries and ankle strength, flexibility, and proprioception in college basketball players","volume":"32","author":"Payne","year":"1997","journal-title":"J. Athl. Train."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1589\/jpts.29.1363","article-title":"Associations between ankle dorsiflexion range of motion and foot and ankle strength in young adults","volume":"29","author":"Emeterio","year":"2017","journal-title":"J. Phys. Ther. Sci."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:57:41Z","timestamp":1760115461000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,31]]},"references-count":33,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["computation13010007"],"URL":"https:\/\/doi.org\/10.3390\/computation13010007","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2024,12,31]]}}}