{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T05:51:17Z","timestamp":1768974677584,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T00:00:00Z","timestamp":1612310400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Actuators"],"abstract":"<jats:p>This article presents an innovative legged-wheeled system, designed to be applied in a hybrid robotic vehicle\u2019s locomotion system, as its driving member. The proposed system will be capable to combine the advantages of legged and wheeled locomotion systems, having 3DOF connected through a combination of both rigid and non-rigid joints. This configuration provides the vehicle the ability to absorb impacts and selected external disturbances. A state space approach was adopted to control the joints, increasing the system\u2019s stability and adaptability. Throughout this article, the entire design process of this robotic system will be presented, as well as its modeling and control. The proposed system\u2019s design is biologically inspired, having as reference the human leg, resulting in the development of a prototype. The results of the testing process with the proposed prototype are also presented. This system was designed to be modular, low-cost, and to increase the autonomy of typical autonomous legged-wheeled locomotion systems.<\/jats:p>","DOI":"10.3390\/act10020029","type":"journal-article","created":{"date-parts":[[2021,2,3]],"date-time":"2021-02-03T20:31:51Z","timestamp":1612384311000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Design, Modeling, and Control of a Single Leg for a Legged-Wheeled Locomotion System with Non-Rigid Joint"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7840-0333","authenticated-orcid":false,"given":"V\u00edtor H.","family":"Pinto","sequence":"first","affiliation":[{"name":"FEUP\u2014Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"CRIIS\u2014Centre for Robotics in Industry and Intelligent Systems, INESC TEC\u2014Institute for Systems and Computer Engineering, Technology and Science, Campus of FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5499-1730","authenticated-orcid":false,"given":"Jos\u00e9","family":"Gon\u00e7alves","sequence":"additional","affiliation":[{"name":"CRIIS\u2014Centre for Robotics in Industry and Intelligent Systems, INESC TEC\u2014Institute for Systems and Computer Engineering, Technology and Science, Campus of FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"CeDRI\u2014Research Centre in Digitalization and Intelligent Robotics, School of Technology and Management Polytechnic Institute of Bragan\u00e7a, Santa Apol\u00f3nia Campus, 5300-253 Bragan\u00e7a, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4846-271X","authenticated-orcid":false,"given":"Paulo","family":"Costa","sequence":"additional","affiliation":[{"name":"FEUP\u2014Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"},{"name":"CRIIS\u2014Centre for Robotics in Industry and Intelligent Systems, INESC TEC\u2014Institute for Systems and Computer Engineering, Technology and Science, Campus of FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1002\/rob.21677","article-title":"NimbRo Rescue: Solving disaster-response tasks with the mobile manipulation robot Momaro","volume":"34","author":"Schwarz","year":"2017","journal-title":"J. Field Robot."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1109\/LRA.2019.2896758","article-title":"CENTAURO: A hybrid locomotion and high power resilient manipulation platform","volume":"4","author":"Kashiri","year":"2019","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hutter, M., Gehring, C., Jud, D., Lauber, A., Bellicoso, C.D., Tsounis, V., Hwangbo, J., Bodie, K., Fankhauser, P., and Bloesch, M. (2016, January 9\u201314). ANYmal\u2014A highly mobile and dynamic quadrupedal robot. Proceedings of the 2016 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Korea.","DOI":"10.1109\/IROS.2016.7758092"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3626","DOI":"10.1109\/LRA.2020.2979661","article-title":"Rolling in the Deep\u2013Hybrid Locomotion for Wheeled-Legged Robots using Online Trajectory Optimization","volume":"5","author":"Bjelonic","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_5","unstructured":"Eich, M., Grimminger, F., Bosse, S., Spenneberg, D., and Kirchner, F. (2009, January 22\u201325). Asguard: A hybrid-wheel security and sar-robot using bio-inspired locomotion for rough terrain. Proceedings of the ROBIO 2008, Bangkok, Thailand."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Shi, Q., Miyagishima, S., Konno, S., Fumino, S., Ishii, H., Takanishii, A., Laschi, C., Mazzolai, B., Mattoli, V., and Dario, P. (2010, January 26\u201329). Development of the hybrid wheel-legged mobile robot WR-3 designed to interact with rats. Proceedings of the 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, Tokyo, Japan.","DOI":"10.1109\/BIOROB.2010.5627719"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Freitas, G., Lizarralde, F., Hsu, L., Paranhos, V., Dos Reis, N.R.S., and Bergerman, M. (2011, January 7\u20139). Design, modeling, and control of a wheel-legged locomotion system for the environmental hybrid robot. Proceedings of the IASTED International Conference, Pittsburgh, Penn.","DOI":"10.2316\/P.2011.752-011"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1109\/TMECH.2013.2253615","article-title":"Quattroped: A leg\u2013wheel transformable robot","volume":"19","author":"Chen","year":"2013","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1109\/TRO.2014.2365651","article-title":"Wheel transformer: A wheel-leg hybrid robot with passive transformable wheels","volume":"30","author":"Kim","year":"2014","journal-title":"IEEE Trans. Robot."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1687814015616908","DOI":"10.1177\/1687814015616908","article-title":"Design and analysis of a wheel-legged hybrid locomotion mechanism","volume":"7","author":"Zheng","year":"2015","journal-title":"Adv. Mech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s10846-015-0303-2","article-title":"A wheel-legged robot with active waist joint: Design, analysis, and experimental results","volume":"83","author":"Qiao","year":"2016","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hu, W., Li, G., Sun, Y., Jiang, G., Kong, J., Ju, Z., and Jiang, D. (2017). A review of upper and lower limb rehabilitation training robot. International Conference on Intelligent Robotics and Applications, Springer.","DOI":"10.1007\/978-3-319-65289-4_54"},{"key":"ref_13","unstructured":"Hu, J., Hou, Z., Zhang, F., Chen, Y., and Li, P. (September, January 28). Training strategies for a lower limb rehabilitation robot based on impedance control. Proceedings of the 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, San Diego, CA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.mechatronics.2015.11.010","article-title":"The design and control of a 3DOF lower limb rehabilitation robot","volume":"33","author":"Wu","year":"2016","journal-title":"Mechatronics"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Feng, Y., Wang, H., Vladareanu, L., Chen, Z., and Jin, D. (2019). New Motion Intention Acquisition Method of Lower Limb Rehabilitation Robot Based on Static Torque Sensors. Sensors, 19.","DOI":"10.3390\/s19153439"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pinto, V.H., Gon\u00e7alves, J., and Costa, P. (2020). Towards a More Robust Non-Rigid Robotic Joint. Appl. Syst. Innov., 3.","DOI":"10.3390\/asi3040045"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Pinto, V.H., Gon\u00e7alves, J., and Costa, P. (2020). Modeling and Control of a DC Motor Coupled to a Non-Rigid Joint. Appl. Syst. Innov., 3.","DOI":"10.3390\/asi3020024"},{"key":"ref_18","unstructured":"Vaccaro, R.J. (1995). Digital Control: A State-Space Approach, McGraw-Hill Higher Education."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1109\/TAC.1978.1101743","article-title":"Computing integrals involving the matrix exponential","volume":"23","year":"1978","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1524\/auto.1972.20.112.297","article-title":"The design of linear control systems in the state space","volume":"20","author":"Ackermann","year":"1972","journal-title":"At-Automatisierungstechnik"}],"container-title":["Actuators"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-0825\/10\/2\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:19:47Z","timestamp":1760159987000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-0825\/10\/2\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,3]]},"references-count":20,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2]]}},"alternative-id":["act10020029"],"URL":"https:\/\/doi.org\/10.3390\/act10020029","relation":{},"ISSN":["2076-0825"],"issn-type":[{"value":"2076-0825","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,3]]}}}