{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T14:38:48Z","timestamp":1773931128536,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"PNRR MUR project","award":["PE0000013-FAIR"],"award-info":[{"award-number":["PE0000013-FAIR"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>In this paper, the locomotion and steering control of a simulated Mini Cheetah quadruped robot was investigated in the presence of terrain characterised by low friction. Low-level locomotion and steering control were implemented via a central pattern generator approach, whereas high-level steering control manoeuvres were implemented by comparing a neural network and a linear model predictive controller in a dynamic simulation environment. A data-driven approach was adopted to identify the robot model using both a linear transfer function and a shallow artificial neural network. The results demonstrate that, whereas the linear approach showed good performance in high-friction terrain, in the presence of slippery conditions, the application of a neural network predictive controller improved trajectory accuracy and preserved robot safety with different steering manoeuvres. A comparative analysis was carried out using several performance indices.<\/jats:p>","DOI":"10.3390\/robotics12030067","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:14:08Z","timestamp":1682943248000},"page":"67","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Data-Driven Model Predictive Control for Quadruped Robot Steering on Slippery Surfaces"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1050-5729","authenticated-orcid":false,"given":"Paolo","family":"Arena","sequence":"first","affiliation":[{"name":"DIEEI, University of Catania, 95125 Catania, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5488-9365","authenticated-orcid":false,"given":"Luca","family":"Patan\u00e8","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Messina, 98122 Messina, Italy"}]},{"given":"Salvatore","family":"Taffara","sequence":"additional","affiliation":[{"name":"DIEEI, University of Catania, 95125 Catania, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,1]]},"reference":[{"key":"ref_1","first-page":"em0133","article-title":"The NAO Robot in Slippery Scenarios: A Strategy","volume":"6","author":"Franco","year":"2021","journal-title":"J. Inf. Syst. Eng. Manag."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Al-Homsy, A., Hartmann, J., and Maehle, E. (2012, January 16\u201318). Slippery and sandy ground detection for hexapod robots based on organic computing principles and somatosensory feedback. Proceedings of the 2012 IEEE International Symposium on Robotic and Sensors Environments Proceedings, Magdeburg, Germany.","DOI":"10.1109\/ROSE.2012.6402620"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"103869","DOI":"10.1016\/j.engappai.2020.103869","article-title":"Reinforcement learning for quadrupedal locomotion with design of continual\u2013hierarchical curriculum","volume":"95","author":"Kobayashi","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Katz, B., Carlo, J.D., and Kim, S. (2019, January 20\u201324). Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control. Proceedings of the 2019 International Conference on Robotics and Automation (ICRA), Montreal, QC, Canada.","DOI":"10.1109\/ICRA.2019.8793865"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/3516.868914","article-title":"Slip detection and control using tactile and force sensors","volume":"5","author":"Melchiorri","year":"2000","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.sna.2014.09.023","article-title":"Development of an optoelectronic 6-axis force\/torque sensor for robotic applications","volume":"220","author":"Palli","year":"2014","journal-title":"Sens. Actuators A Phys."},{"key":"ref_7","unstructured":"Focchi, M., Barasuol, V., Frigerio, M., Caldwell, D., and Semini, C. (2015, January 12\u201315). Slip Detection and Recovery for Quadruped Robots. Proceedings of the ISRR, Sestri Levante, Italy."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1327","DOI":"10.1007\/s00170-021-07682-3","article-title":"Review on model predictive control: An engineering perspective","volume":"117","author":"Schwenzer","year":"2021","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Cho, J., and Park, J.H. (2022). RModel Predictive Control of Running Biped Robot. Appl. Sci., 12.","DOI":"10.3390\/app122111183"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"145710","DOI":"10.1109\/ACCESS.2021.3118957","article-title":"Model predictive control with environment adaptation for legged locomotion","volume":"9","author":"Rathod","year":"2021","journal-title":"IEEE Access"},{"key":"ref_11","first-page":"1","article-title":"From linear to nonlinear MPC: Bridging the gap via the real-time iteration","volume":"93","author":"Gros","year":"2016","journal-title":"Int. J. Control."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1109\/LRA.2018.2800124","article-title":"Whole-Body Nonlinear Model Predictive Control through Contacts for Quadrupeds","volume":"3","author":"Neunert","year":"2018","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1109\/LRA.2023.3246839","article-title":"Real-Time Neural MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms","volume":"8","author":"Salzmann","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.jprocont.2006.06.001","article-title":"A neural network model predictive controller","volume":"16","author":"Toivonen","year":"2006","journal-title":"J. Process. Control"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Laurenzi, A., Hoffman, E.M., and Tsagarakis, N.G. (2018, January 1\u20135). Quadrupedal walking motion and footstep placement through Linear Model Predictive Control. Proceedings of the 2018 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Madrid, Spain.","DOI":"10.1109\/IROS.2018.8593692"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Adamatzky, A., and Chen, G. (2013). Chaos, CNN, Memristors and Beyond, World Scientific.","DOI":"10.1142\/8590"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1109\/81.747195","article-title":"Reaction-diffusion CNN algorithms to generate and control artificial locomotion","volume":"46","author":"Arena","year":"1999","journal-title":"IEEE Trans. Circuits Syst. Fundam. Theory Appl."},{"key":"ref_18","unstructured":"Arena, P., Castorina, S., Fortuna, L., Frasca, M., and Ruta, M. (2003, January 25\u201328). A CNN-based chip for robot locomotion control. Proceedings of the 2003 IEEE International Symposium on Circuits and Systems (ISCAS), Bangkok, Thailand."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2212","DOI":"10.1109\/TCST.2021.3131119","article-title":"A New Embodied Motor-Neuron Architecture","volume":"30","author":"Arena","year":"2022","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.ifacol.2021.11.031","article-title":"A data-driven neural network model predictive steering controller for a bio-inspired quadruped robot","volume":"54","author":"Arena","year":"2021","journal-title":"IFAC-PapersOnLine"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF00319514","article-title":"Mechanisms of frequency and pattern control in the neural rhythm generators","volume":"56","author":"Matsuoka","year":"1987","journal-title":"Biol. Cybern."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"91587","DOI":"10.1109\/ACCESS.2020.2992794","article-title":"Bio-Inspired Adaptive Locomotion Control System for Online Adaptation of a Walking Robot on Complex Terrains","volume":"8","author":"Ngamkajornwiwat","year":"2020","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s00422-016-0708-4","article-title":"A sensory-driven controller for quadruped locomotion","volume":"111","author":"Ferreira","year":"2017","journal-title":"Biol. Cybern."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/j.neuron.2006.11.008","article-title":"Biological Pattern Generation: The Cellular and Computational Logic of Networks in Motion","volume":"52","author":"Grillner","year":"2006","journal-title":"Neuron"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Arena, P., and Patan\u00e8, L. (2014). Spatial Temporal Patterns for Action-Oriented Perception in Roving Robots II, an Insect Brain Computational Model, Springer. Cognitive Systems Monographs.","DOI":"10.1007\/978-3-319-02362-5"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Dennis, J.E., and Schnabel, R.B. (1996). Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16), Society for Industrial & Applied Math.","DOI":"10.1137\/1.9781611971200"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4024","DOI":"10.1109\/TIT.2017.2717599","article-title":"Bridging AIC and BIC: A New Criterion for Autoregression","volume":"64","author":"Ding","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Karimi, M. (2007, January 24\u201327). Finite Sample AIC for Autoregressive Model Order Selection. Proceedings of the 2007 IEEE International Conference on Signal Processing and Communications, Dubai, United Arab Emirates.","DOI":"10.1109\/ICSPC.2007.4728545"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1109\/TIT.2021.3050469","article-title":"Goodness-of-Fit Tests on Manifolds","volume":"67","author":"Shapiro","year":"2021","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Chimitova, E.V., and Chetvertakova, E.S. (2018, January 2\u20136). Goodness-of-Fit Testing for the Degradation Models in Reliability Analysis. Proceedings of the 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE), Novosibirsk, Russia.","DOI":"10.1109\/APEIE.2018.8546176"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Rohmer, E., Singh, S.P.N., and Freese, M. (2013, January 3\u20137). V-REP: A versatile and scalable robot simulation framework. Proceedings of the 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan.","DOI":"10.1109\/IROS.2013.6696520"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/3\/67\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:27:57Z","timestamp":1760124477000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/3\/67"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,1]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["robotics12030067"],"URL":"https:\/\/doi.org\/10.3390\/robotics12030067","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,5,1]]}}}