{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T02:11:59Z","timestamp":1784340719964,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T00:00:00Z","timestamp":1623974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Autonomous vehicles are nowadays one of the most important technologies that will be incorporated to every day life in the next few years. One of the most promising kind of vehicles in terms of efficiency and sustainability are those known as Wing-in-Ground crafts, or WIG crafts, a family of vehicles that seize the proximity of ground to achieve a flight with low drag and high lift. However, this kind of crafts lacks of a sound theory of flight that can lead to robust control solutions that guarantees safe autonomous operation in all the cruising phases.In this paper we address the problem of controlling a WIG craft in different scenarios and using different control strategies in order to compare their performance. The tested scenarios include obstacle avoidance by fly over and recovering from a random disturbance in vehicle attitude. MPC (Model Predictive Control) is tested on the complete nonlinear model, while PID, used as baseline controller, LQR (Linear Quadratic Regulator) and adaptive LQR are tested on top of a partial feedback linearization. Results show that LQR has got the best overall performance, although it is seen that different design specifications could lead to the selection of one controller or another.<\/jats:p>","DOI":"10.3390\/s21124193","type":"journal-article","created":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T11:19:20Z","timestamp":1624015160000},"page":"4193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Nonlinear Control Strategies for an Autonomous Wing-In-Ground-Effect Vehicle"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3418-3784","authenticated-orcid":false,"given":"Davide","family":"Patria","sequence":"first","affiliation":[{"name":"Politecnico Di Torino, 10129 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8740-2453","authenticated-orcid":false,"given":"Claudio","family":"Rossi","sequence":"additional","affiliation":[{"name":"Centre for Automation and Robotics UPM-CSIC, Universidad Polit\u00e9cnica de Madrid, 28006 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4102-5899","authenticated-orcid":false,"given":"Ramon A. Suarez","family":"Fernandez","sequence":"additional","affiliation":[{"name":"Centre for Automation and Robotics UPM-CSIC, Universidad Polit\u00e9cnica de Madrid, 28006 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9498-5407","authenticated-orcid":false,"given":"Sergio","family":"Dominguez","sequence":"additional","affiliation":[{"name":"Centre for Automation and Robotics UPM-CSIC, Universidad Polit\u00e9cnica de Madrid, 28006 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,18]]},"reference":[{"key":"ref_1","unstructured":"Undisclosed (2017). Motorways of the Sea: An Ex Post Evaluation on the Development of the Concept from 2001 and Possible Ways Forwarded, European Commission. Technical Report."},{"key":"ref_2","first-page":"10027","article-title":"Review on the cost and performance of a WIGE craft: A commercialization prospective","volume":"10","author":"Yin","year":"2015","journal-title":"ARPN J. Eng. Appl. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Yun, L., Bliault, A., and Doo, J. (2010). WIG Craft and Ekranoplan, Springer.","DOI":"10.1007\/978-1-4419-0042-5"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Cui, E., and Zhang, X. (2010). Ground Effect Aerodynamics, John Wiley & Sons. Chapter 18.","DOI":"10.1002\/9780470686652.eae022"},{"key":"ref_5","unstructured":"Korhonen, P. (2007). Toivo Kaario (1912\u20131970) Pintakulkuneuvojen Kehitt\u00e4j\u00e4n\u00e4 (Toivo Kaario (1912\u20131970) as a Developer of Surface Vehicles). [Master\u2019s Thesis, Historiatieteen Laitos (Department of History)]."},{"key":"ref_6","unstructured":"Undisclosed (1972). Low-Speed Longitudinal Aerodynamic Characteristics of Aircraft in Ground Effect, Engineering Sciences Data Unit. Technical Report."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kim, S. (2001). Design Optimizacion of High-Lift Configurations Using a Viscous Adjoint-Based Method. [Ph.D. Thesis, Stanford University].","DOI":"10.2514\/6.2002-844"},{"key":"ref_8","unstructured":"Hean, N. (2005). Wing in Ground (WIG) Aircraft Aerodynamics. [Master\u2019s Thesis, National University of Singapore]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"913","DOI":"10.2514\/1.C032531","article-title":"Numerical study of aerodynamics of a wing-in-ground-effect craft","volume":"51","author":"Qu","year":"2014","journal-title":"J. Aircr."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"29","DOI":"10.2514\/1.J057544","article-title":"Stability of low-Reynolds-number separated flos around an airfoil near a wavy ground","volume":"57","author":"He","year":"2019","journal-title":"AIAA J."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Hu, H., and Ma, D. (2020). Airfoil aerodynamics in proximity to wavy ground for a wide range of angles of attack. Appl. Sci., 10.","DOI":"10.3390\/app10196773"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Baddoo, P., Kurt, M., Ayton, L., and Moored, K. (2020). Exact solutions for ground effect. J. Fluid Mech., 891.","DOI":"10.1017\/jfm.2020.149"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xie, J., Song, L., Huang, J., and Fu, J. (2021). Parameter study on lateral moments of banked wings in ground effect. Chin. J. Aeronaut.","DOI":"10.1016\/j.cja.2021.03.024"},{"key":"ref_14","unstructured":"Hahn, T., Drewelow, W., Dewitz, D., Kolewe, B., and Lampe, B. (2020, January 24\u201329). Analysis of wing-in-ground-effect vehicle with regard to safety ensuring control. Proceedings of the 19th World Congress of The International Federation of Automatic Control, Cape Town, South Africa."},{"key":"ref_15","unstructured":"Irodov, R. (1974). Criteria of the Longitudinal Stability of the Ekranoplan, National Technical Information Service, U.S. Department of Commerce."},{"key":"ref_16","unstructured":"Boschetti, P., and C\u00e1rdenas, E. (2020, January 9\u201312). Ground effect on the longitudinal stability of an unmanned airplane. Proceedings of the 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.proeng.2013.12.002","article-title":"Computational aerodynamics and flight stability of Wing-In-Ground (WIG) craft","volume":"67","author":"Wang","year":"2013","journal-title":"Procedia Eng."},{"key":"ref_18","unstructured":"De Divitiis, N. (2009). Performance and Statility of a Winged Vehicle y Ground Effect, University of Rome \u201cLa Sapienza\u201d. Technical Report."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1080\/09377255.2020.1724647","article-title":"Influence of ground effect on lingitudinal aerodynamic damping of wing in ground effect vehicles","volume":"67","author":"Shabarov","year":"2020","journal-title":"Ship Technol. Res."},{"key":"ref_20","first-page":"1134","article-title":"Aerodynaimc and static stability characteristics of airfoils in extreme ground effect","volume":"232","author":"Nirooei","year":"2018","journal-title":"J. Aerosp. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1515\/ijnaoe-2015-0018","article-title":"Longitudinal static stability requirements for wing in ground effect vehicle","volume":"7","author":"Yang","year":"2015","journal-title":"Int. J. Naval Archit. Ocean Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Dantsecivh, I., Prasolov, V., and Lyutikova, M. (2020, January 28\u201329). Research of wing in surface effect ship configuration and development of an experimental model of increased stability. Proceedings of the IOP Conference Series: Materials Science and Engineering, Stavropol, Russian Federation.","DOI":"10.1088\/1757-899X\/873\/1\/012029"},{"key":"ref_23","unstructured":"Qihui, L. (2006). Stability, Control and Performance for an Inverted Delta Wing-In-Ground Effect Aircraft. [Master\u2019s Thesis, National University of Singapore]."},{"key":"ref_24","unstructured":"Nebylov, A., and Nebylov, V. (2017, January 3\u20136). WIG-craft flight control concept for the waved sea. Proceedings of the 7th European Conference for Aeronautics and Space Sciences, Milano, Italy."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Matdaud, Z., Zhahir, A., Afifi, A., and Ahmad, M. (2019, January 26\u201327). Stabilizing attitude control for mobility of wing in ground (WIG) craft\u2014A review. Proceedings of the IOP Conference Series: Materials Science and Engineering, Kuala Lumpur, Malaysia.","DOI":"10.1088\/1757-899X\/642\/1\/012005"},{"key":"ref_26","unstructured":"Astrom, K., and Wittenmark, B. (2008). Adaptive Control, Dover Publications Inc."},{"key":"ref_27","first-page":"3660","article-title":"Flight PID controller design for a UAV quadrotor","volume":"5","author":"Salih","year":"2010","journal-title":"Sci. Res. Essays"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Camacho, E., and Bordons, C. (2007). Model Predictive Control, Springer. [2nd ed.].","DOI":"10.1007\/978-0-85729-398-5"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.conengprac.2016.12.009","article-title":"Rapid development of modular and sustainable nonlinear model predictive control solutions","volume":"60","author":"Lucia","year":"2017","journal-title":"Control Eng. Pract."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12532-018-0139-4","article-title":"CasADi\u2014A software framework for nonlinear optimization and optimal control","volume":"11","author":"Andersson","year":"2019","journal-title":"Math. Program. Comput."},{"key":"ref_31","unstructured":"Khalil, H. (2002). Nonlinear Systems, Prentice Hall."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4193\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:18:31Z","timestamp":1760163511000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,18]]},"references-count":31,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21124193"],"URL":"https:\/\/doi.org\/10.3390\/s21124193","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,18]]}}}