{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T17:28:21Z","timestamp":1783013301116,"version":"3.54.6"},"reference-count":36,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>In this paper, a robust geometric navigation algorithm, designed on the special Euclidean group SE(3), of a quadrotor is proposed. The equations of motion for the quadrotor are obtained using the Newton\u2013Euler formulation. The geometric navigation considers a guidance frame which is designed to perform autonomous flights with a convergence to the contour of the task with small normal velocity. For this purpose, a super twisting algorithm controls the nonlinear rotational and translational dynamics as a cascade structure in order to establish the fast and yet smooth tracking with the typical robustness of sliding modes. In this sense, the controller provides robustness against parameter uncertainty, disturbances, convergence to the sliding manifold in finite time, and asymptotic convergence of the trajectory tracking. The algorithm validation is presented through experimental results showing the feasibility of the proposed approach and illustrating that the tracking errors converge asymptotically to the origin.<\/jats:p>","DOI":"10.1017\/s0263574719001231","type":"journal-article","created":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T09:00:17Z","timestamp":1564995617000},"page":"1019-1040","source":"Crossref","is-referenced-by-count":15,"title":["Robust Geometric Navigation of a Quadrotor UAV on SE(3)"],"prefix":"10.1017","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0445-1541","authenticated-orcid":false,"given":"O.","family":"Garcia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8156-3512","authenticated-orcid":false,"given":"E. G.","family":"Rojo-Rodriguez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Sanchez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Saucedo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5125-2644","authenticated-orcid":false,"given":"A. J.","family":"Munoz-Vazquez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2019,8,5]]},"reference":[{"key":"S0263574719001231_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2011.10.017"},{"key":"S0263574719001231_ref9","doi-asserted-by":"publisher","DOI":"10.2514\/1.55226"},{"key":"S0263574719001231_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2018.05.009"},{"key":"S0263574719001231_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-017-0547-0"},{"key":"S0263574719001231_ref24","doi-asserted-by":"crossref","first-page":"3974","DOI":"10.1109\/TLA.2016.7785921","article-title":"Embedded super twisting control for the attitude of a quadrotor,","volume":"14","author":"Escobar","year":"2016","journal-title":"IEEE Latin America Trans"},{"key":"S0263574719001231_ref2","volume-title":"Unmanned Aerial Vehicles Embedded Control","author":"Lozano","year":"2010"},{"key":"S0263574719001231_ref35","unstructured":"[35] Bristeau, P. J. , Callou, F. , Vissiere, D. and Petit, N. , \u201cThe Navigation and Control Technology Inside the AR.Drone Micro UAV,\u201d Proceedings of the 18th IFAC World Congress, Milano, Italy (2011) pp. 1477\u20131484."},{"key":"S0263574719001231_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2016.08.111"},{"key":"S0263574719001231_ref30","volume-title":"Differential Inclusions: Set-Valued Maps and Viability Theory","author":"Aubin","year":"2012"},{"key":"S0263574719001231_ref10","unstructured":"[10] Pylorof, D. and Bakolas, E. , \u201cTracking a Maneuvering Target with an Underactuated UAV in the SE(3) Space,\u201d AIAA Guidance, Navigation, and Control Conference, AIAA SciTech Forum (2015) pp. 1\u201312."},{"key":"S0263574719001231_ref28","doi-asserted-by":"publisher","DOI":"10.1109\/ROPEC.2015.7395094"},{"key":"S0263574719001231_ref33","unstructured":"[33] Frazzoli, E. , Dahleh, M. A. and Ferron, E. , \u201cTrajectory Tracking Control Design for Autonomous Helicopters Using a Backstepping Algorithm,\u201d Proceedings of the IEEE American Control Conference (ACC), Chicago IL (2000) pp. 4102\u20134107."},{"key":"S0263574719001231_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2009.11.008"},{"key":"S0263574719001231_ref5","unstructured":"[5] Lee, T. , Leok, M. and McClamroch, N. H. , \u201cGeometric Tracking Control of a Quadrotor UAV on SE(3),\u201d Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA (2010) pp. 5420\u20135425."},{"key":"S0263574719001231_ref6","doi-asserted-by":"publisher","DOI":"10.1002\/asjc.567"},{"key":"S0263574719001231_ref16","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2016.7798991"},{"key":"S0263574719001231_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.paerosci.2017.09.001"},{"key":"S0263574719001231_ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2186179"},{"key":"S0263574719001231_ref36","first-page":"1","article-title":"Test bed for applications of heterogeneous unmanned vehicles,","volume":"14","author":"Munoz Palacios","year":"2017","journal-title":"Int. J. Adv. Robot. Syst. (IJARS)"},{"key":"S0263574719001231_ref14","unstructured":"[14] Nazari, M. , Maadani, M. , Butcher, E. A. and Yucelen, T. , \u201cMorse-Lyapunov-Based Control of Rigid Body Motion on TSE(3) via Backstepping,\u201d 2018 AIAA Guidance, Navigation and Control Conference, AIAA SciTech Forum (2018) pp. 1\u201312."},{"key":"S0263574719001231_ref15","doi-asserted-by":"publisher","DOI":"10.1109\/MRA.2012.2206474"},{"key":"S0263574719001231_ref11","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.3399"},{"key":"S0263574719001231_ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.07.002"},{"key":"S0263574719001231_ref23","first-page":"1","article-title":"Position-yaw tracking of quadrotors,","volume":"137","author":"Sanchez","year":"2015","journal-title":"J. Dyn. Syst. Measurement Control"},{"key":"S0263574719001231_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2011.10.011"},{"key":"S0263574719001231_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-7276-7"},{"key":"S0263574719001231_ref3","unstructured":"[3] Sanchez, A. , Parra-Vega, V. , Garcia, O. , Ruiz-Sanchez, F. and Ramos-Velasco, L. E. , \u201cTime-Parametrization Control of Quadrotors with a Robust Quaternion-based Sliding Mode Controller for Aggressive Maneuvering,\u201d 2013 European Control Conference (ECC), Zurich, Switzerland (2013) pp. 3876\u20133881."},{"key":"S0263574719001231_ref26","volume-title":"Flight Dynamics","author":"Stengel","year":"2004"},{"key":"S0263574719001231_ref17","doi-asserted-by":"publisher","DOI":"10.3390\/en12081551"},{"key":"S0263574719001231_ref13","unstructured":"[13] Viswanathan, S. P. , Sanyal, A. K. and Izadi, M. , \u201cIntegrated Guidance and Nonlinear Feedback Control of Underactuated Unmanned Aerial Vehicles in SE(3),\u201d AIAA Guidance, Navigation and Control Conference, AIAA SciTech Forum (2017) pp. 1\u201312."},{"key":"S0263574719001231_ref19","unstructured":"[19] Jayakrishnan, H. J. , \u201cPosition and Attitude Control of a Quadrotor UAV Using Super Twisting Sliding Mode,\u201d IFAC 2016 (2016) pp. 284\u2013289."},{"key":"S0263574719001231_ref27","volume-title":"Principles of Helicopter Aerodynamics","author":"Leishman","year":"2006"},{"key":"S0263574719001231_ref4","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2009.5159850"},{"key":"S0263574719001231_ref20","unstructured":"[20] Bouchoucha, M. , Seghour, S. and Tadjine, M. , \u201cClassical and Second Order Sliding Mode Control Solution to an Attitude Stabilization of a Four Rotors helicopter: From Theory to Experiment,\u201d 2011 IEEE International Conference on Mechatronics (ICM), Istanbul, Turkey (2011)."},{"key":"S0263574719001231_ref8","unstructured":"[8] Colorado, J. , Barrientos, A. , Martinez, A. , Lafaverges, B. and Valente, J. , \u201cMini-Quadrotor Attitude Control Based on Hybrid Backstepping and Frenet\u2013Serret Theory,\u201d Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010), Anchorage, AK (2010) pp. 1617\u20131622."},{"key":"S0263574719001231_ref25","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574718000516"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574719001231","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,28]],"date-time":"2020-04-28T10:18:14Z","timestamp":1588069094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574719001231\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,5]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["S0263574719001231"],"URL":"https:\/\/doi.org\/10.1017\/s0263574719001231","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,5]]}}}