{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T16:45:19Z","timestamp":1783010719743,"version":"3.54.6"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Unmanned aerial vehicle (UAV) technology has recently experienced increasing development, leading to the creation of a wide variety of autonomous solutions. In this paper, a guidance strategy for straight and orbital paths following fixed-wing small UAVs is presented. The proposed guidance algorithm is based on a reference vector field as desired, with 16 courses for the UAV to follow. A sliding mode approach is implemented to improve the robustness and effectiveness, and the asymptotic convergence of the aircraft to the desired trajectory in the presence of constant wind disturbances is proved according to Lyapunov. The algorithm exploits the banking dynamics and generates reference signals for the inner-loop aileron control. A MATLAB&amp;Simulink\u00ae simulation environment is used to verify the performance and robustness of the compared guidance algorithms. This high-fidelity model considers the six-degrees-of-freedom (DoF) whole-flight dynamics of the UAV and it is based on experimental flight test data to implement the aerodynamic behavior.<\/jats:p>","DOI":"10.3390\/robotics14010007","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T07:59:42Z","timestamp":1736409582000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Sliding Mode Approach to Vector Field Path Following for a Fixed-Wing UAV"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7385-9471","authenticated-orcid":false,"given":"Luca","family":"Pugi","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, Universit\u00e0 degli Studi di Firenze, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lorenzo","family":"Franchi","sequence":"additional","affiliation":[{"name":"Sky Eye Systems SRL, 56021 Cascina, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuele","family":"Favilli","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Universit\u00e0 degli Studi di Firenze, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4928-1099","authenticated-orcid":false,"given":"Giuseppe","family":"Mattei","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Universit\u00e0 degli Studi di Firenze, 50139 Firenze, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1109\/MCS.2013.2287568","article-title":"Unmanned aerial vehicle path following: A survey and analysis of algorithms for fixed-wing unmanned aerial vehicles","volume":"34","author":"Sujit","year":"2014","journal-title":"IEEE Control. Syst. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/S1474-6670(17)32021-9","article-title":"Dynamic 3D path following for an autonomous helicopter","volume":"37","author":"Conte","year":"2004","journal-title":"IFAC Proc. Vol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"980","DOI":"10.1109\/TCST.2009.2014359","article-title":"Path generation and tracking in 3-D for UAVs","volume":"17","author":"Ambrosino","year":"2009","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/s11424-018-8006-y","article-title":"Vector field based sliding mode control of curved path following for miniature unmanned aerial vehicles in winds","volume":"31","author":"Wang","year":"2018","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12985","DOI":"10.3182\/20110828-6-IT-1002.03720","article-title":"Adaptive optimal path following for high wind flights","volume":"44","author":"Ratnoo","year":"2011","journal-title":"IFAC Proc. Vol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1109\/TAC.2006.890484","article-title":"Path-following for nonlinear systems with unstable zero dynamics","volume":"52","author":"Dacic","year":"2007","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.1109\/TAC.2008.928309","article-title":"An Improved Path-Following Method for Mixed H2\/H\u221e Controller Design","volume":"53","author":"Ostertag","year":"2008","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1109\/TRO.2007.898976","article-title":"Vector field path following for miniature air vehicles","volume":"23","author":"Nelson","year":"2007","journal-title":"IEEE Trans. Robot."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1109\/TCST.2014.2303787","article-title":"Fixed wing UAV path following in wind with input constraints","volume":"22","author":"Beard","year":"2014","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/TCST.2014.2322773","article-title":"Guidance of air vehicles: A sliding mode approach","volume":"23","author":"Shah","year":"2014","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.ast.2015.11.033","article-title":"Lateral guidance and control of UAVs using second-order sliding modes","volume":"49","author":"Ali","year":"2016","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chen, P., Zhang, G., Li, J., Chang, Z., and Yan, Q. (2023). Path-Following Control of Small Fixed-Wing UAVs under Wind Disturbance. Drones, 7.","DOI":"10.3390\/drones7040253"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1109\/TRO.2004.837240","article-title":"Path-following control of mobile robots in presence of uncertainties","volume":"21","author":"Coelho","year":"2005","journal-title":"IEEE Trans. Robot."},{"key":"ref_14","first-page":"2016416","article-title":"Robust integral terminal sliding mode control for quadrotor UAV with external disturbances","volume":"2019","author":"Labbadi","year":"2019","journal-title":"Int. J. Aerosp. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.isatra.2022.11.027","article-title":"2-D path following for fixed wing UAV using global fast terminal sliding mode control","volume":"136","author":"Nian","year":"2023","journal-title":"ISA Trans."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1109\/TAC.2007.902731","article-title":"Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty","volume":"52","author":"Aguiar","year":"2007","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Casazza, A., Fiorenzani, R., Mela, A., Pugi, L., and Reatti, A. (2021). Modelling of Unmanned Aerial Vehicles with Vertical Take off and Landing Capabilities. International Workshop IFToMM for Sustainable Development Goals, Springer.","DOI":"10.1007\/978-3-030-87383-7_28"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Beard, R.W., and McLain, T.W. (2012). Small Unmanned Aircraft: Theory and Practice, Princeton University Press.","DOI":"10.1515\/9781400840601"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rysdyk, R. (2003, January 15\u201318). UAV path following for constant line of-sight. Proceedings of the 2nd AIAA \u201cUnmanned Unlimited\u201d Conference and Workshop and Exhibit, San Diego, CA, USA.","DOI":"10.2514\/6.2003-6626"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1718","DOI":"10.2514\/1.28957","article-title":"Performance and lyapunov stability of a nonlinear path following guidance method","volume":"30","author":"Park","year":"2007","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Machmudah, A., Shanmugavel, M., Parman, S., Manan TS, A., Dutykh, D., Beddu, S., and Rajabi, A. (2022). Flight Trajectories Optimization of Fixed-Wing UAV by Bank-Turn Mechanism. Drones, 6.","DOI":"10.3390\/drones6030069"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kim, K.J., Park, J.B., and Choi, Y.H. (2006, January 18\u201321). Chattering free sliding mode control. Proceedings of the 2006 SICE-ICASE International Joint Conference, Busan, Republic of Korea.","DOI":"10.1109\/SICE.2006.315237"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.ifacol.2016.10.177","article-title":"A nonlinear model-based wind velocity observer for unmanned aerial vehicles","volume":"49","author":"Borup","year":"2016","journal-title":"IFAC-PapersOnLine"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Beard, R.W., and Humpherys, J. (July, January 29). Following straight line and orbital paths with input constraints. Proceedings of the 2011 American Control Conference, San Francisco, CA, USA.","DOI":"10.1109\/ACC.2011.5990840"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1108\/00022660910926890","article-title":"UAVs and simulation: An experience on MAVs","volume":"81","author":"Capello","year":"2009","journal-title":"Aircr. Eng. Aerosp. Technol."},{"key":"ref_26","unstructured":"McLain, T., Beard, R.W., and Owen, M. (2014). Implementing dubins airplane paths on fixed-wing uavs. Handbook of Unmanned Aerial Vehicles, Springer. Chapter 68."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"652","DOI":"10.3846\/transport.2019.11741","article-title":"Autonomous unmanned aerial vehicle flight accuracy evaluation for three different path-tracking algorithms","volume":"34","author":"Kikutis","year":"2019","journal-title":"Transport"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"102815","DOI":"10.1016\/j.simpat.2023.102815","article-title":"An obstacle avoidance approach for UAV path planning","volume":"129","author":"Bashir","year":"2023","journal-title":"Simul. Model. Pract. Theory"}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:25:43Z","timestamp":1759919143000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/14\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,9]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["robotics14010007"],"URL":"https:\/\/doi.org\/10.3390\/robotics14010007","relation":{},"ISSN":["2218-6581"],"issn-type":[{"value":"2218-6581","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,9]]}}}