{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:16:29Z","timestamp":1775794589122,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T00:00:00Z","timestamp":1656460800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T00:00:00Z","timestamp":1656460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s11071-022-07632-y","type":"journal-article","created":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T08:03:00Z","timestamp":1656489780000},"page":"479-495","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Inner-outer feedback linearization for quadrotor control: two-step design and validation"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7201-6939","authenticated-orcid":false,"given":"Lu\u00eds","family":"Martins","sequence":"first","affiliation":[]},{"given":"Carlos","family":"Cardeira","sequence":"additional","affiliation":[]},{"given":"Paulo","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,29]]},"reference":[{"key":"7632_CR1","doi-asserted-by":"publisher","first-page":"1695","DOI":"10.1007\/s11071-017-3759-8","volume":"90","author":"M Kabiri","year":"2017","unstructured":"Kabiri, M., Atrianfar, H., Menhaj, M.B.: Trajec-tory tracking of a class of under-actuated thrust-propelled vehicle with uncertainties and unknown disturbances. Nonlinear Dyn. 90, 1695\u20131706 (2017)","journal-title":"Nonlinear Dyn."},{"key":"7632_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2020.105716","volume":"98","author":"Z Hou","year":"2020","unstructured":"Hou, Z., Lu, P., Tu, Z.: Nonsingular terminal sliding mode control for a quadrotor UAV with a total rotor failure. Aerosp. Sci. Technol. 98, 105716 (2020)","journal-title":"Aerosp. Sci. Technol."},{"key":"7632_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ast.2020.105744","volume":"99","author":"B Wang","year":"2020","unstructured":"Wang, B., Yu, X., Mu, L., Zhang, Y.: A dual adaptive fault-tolerant control for a quadrotor helicopter against actuator faults and model uncertainties without overestimation. Aerosp. Sci. Technol. 99, 105744 (2020)","journal-title":"Aerosp. Sci. Technol."},{"key":"7632_CR4","doi-asserted-by":"publisher","first-page":"2583","DOI":"10.1007\/s11071-020-06050-2","volume":"102","author":"Z Zhao","year":"2020","unstructured":"Zhao, Z., Cao, D., Yang, J., Wang, H.: High-order sliding mode observer-based trajectory tracking control for a quadrotor UAV with uncertain dynamics. Nonlinear Dyn. 102, 2583\u20132596 (2020)","journal-title":"Nonlinear Dyn."},{"key":"7632_CR5","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1007\/s11071-017-3514-1","volume":"89","author":"C Li","year":"2017","unstructured":"Li, C., Zhang, Y., Li, P.: Full control of a quadrotor using parameter-scheduled backstepping method: implementation and experimental tests. Nonlinear Dyn. 89, 1259\u20131278 (2017)","journal-title":"Nonlinear Dyn."},{"key":"7632_CR6","doi-asserted-by":"publisher","first-page":"3449","DOI":"10.1007\/s11071-020-05671-x","volume":"100","author":"HE Glida","year":"2020","unstructured":"Glida, H.E., Abdou, L., Chelihi, A., Sentouh, C., et al.: Optimal model-free backstepping control for a quadrotor helicopter. Nonlinear Dyn. 100, 3449\u20133468 (2020)","journal-title":"Nonlinear Dyn."},{"key":"7632_CR7","doi-asserted-by":"crossref","unstructured":"Martins, L., Cardeira, C., Oliveira, P.: Global Trajectory Tracking for Quadrotors: An MRP-Based Hybrid Backstepping Strategy In: 2021 60th IEEE Conference on Decision and Control (CDC) (2021), 5759-5764","DOI":"10.1109\/CDC45484.2021.9683107"},{"key":"7632_CR8","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1007\/s11071-019-04859-0","volume":"99","author":"A Eskandarpour","year":"2020","unstructured":"Eskandarpour, A., Sharf, I.: A constrained errorbased MPC for path following of quadrotor with stability analysis. Nonlinear Dyn. 99, 899\u2013918 (2020)","journal-title":"Nonlinear Dyn."},{"key":"7632_CR9","doi-asserted-by":"publisher","first-page":"5413","DOI":"10.3182\/20110828-6-IT-1002.02016","volume":"44","author":"A Freddi","year":"2011","unstructured":"Freddi, A., Lanzon, A., Longhi, S.: A feedback linearization approach to fault tolerance in quadrotor vehicles. IFAC Proc. 44, 5413\u20135418 (2011)","journal-title":"IFAC Proc."},{"key":"7632_CR10","doi-asserted-by":"crossref","unstructured":"Wang, J. et al. Attitude Free Position Control of a Quadcopter Using Dynamic Inversion. Infotech @ Aerospace 2011 (2011)","DOI":"10.2514\/6.2011-1583"},{"key":"7632_CR11","doi-asserted-by":"crossref","unstructured":"Roza, A., Maggiore, M.: Path Following Controller for a Quadrotor Helicopter In: 2012 American Control Conference (ACC) (2012), 4655-466","DOI":"10.1109\/ACC.2012.6315061"},{"key":"7632_CR12","unstructured":"Bonna, R., Camino, J.: Trajectory Tracking Control of a Quadrotor Using Feedback Linearization In: International Symposium on Dynamic Problems of Mechanics (2015)"},{"key":"7632_CR13","first-page":"51","volume":"22","author":"MA Vallejo-Alarcon","year":"2020","unstructured":"Vallejo-Alarcon, M.A.: Robust backstepping control for highly demanding quadrotor flight. J. Control Eng. Appl. Inform. 22, 51\u201362 (2020)","journal-title":"J. Control Eng. Appl. Inform."},{"key":"7632_CR14","doi-asserted-by":"crossref","unstructured":"Aboudonia, A., El-Badawy, A., Rashad, R.: Disturbance observer-based feedback linearization control of an unmanned quadrotor helicopter Proceedings of the Institution of Mechanical Engineers, Part I. J. Syst. Control Eng. 230, 877\u2013891 (2016)","DOI":"10.1177\/0959651816656951"},{"key":"7632_CR15","doi-asserted-by":"crossref","unstructured":"Martins, L., Cardeira, C., Oliveira, P.: Feedback Linearization with Zero Dynamics Stabilization for Quadrotor Control. J. Intell. & Robotic Syst. 101, 1\u201317 (2021)","DOI":"10.1007\/s10846-020-01265-2"},{"key":"7632_CR16","doi-asserted-by":"publisher","first-page":"2555","DOI":"10.1109\/TAC.2011.2108490","volume":"56","author":"CG Mayhew","year":"2011","unstructured":"Mayhew, C.G., Sanfelice, R.G., Teel, A.R.: Quaternion-Based Hybrid Control for Robust Global Attitude Tracking. IEEE Trans. Autom. Control 56, 2555\u20132566 (2011)","journal-title":"IEEE Trans. Autom. Control"},{"key":"7632_CR17","doi-asserted-by":"crossref","unstructured":"Martins, L., Cardeira, C., Oliveira, P.: Linear Quadratic Regulator for Trajectory Tracking of a Quadrotor. IFAC-PapersOnLine 52. In: 21st IFAC Symposium on Automatic Control in Aerospace ACA 2019, 176-181. issn: 2405-8963 (2019)","DOI":"10.1016\/j.ifacol.2019.11.195"},{"key":"7632_CR18","unstructured":"Stengel, R.: Optimal Control and Estimation (Dover Publications, 1994)"},{"key":"7632_CR19","doi-asserted-by":"crossref","unstructured":"Das, A., Subbarao, K., Lewis, F.: Dynamic Inversion of Quadrotor with Zero-Dynamics Stabilization. In: 2008 IEEE International Conference on Control Applications (2008)","DOI":"10.1109\/CCA.2008.4629582"},{"key":"7632_CR20","unstructured":"Leishman, J. G.: Principles of Helicopter Aerodynamics (Cambridge University Press, 2000)"},{"key":"7632_CR21","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1109\/MRA.2012.2206474","volume":"19","author":"R Mahony","year":"2012","unstructured":"Mahony, R., Kumar, V., Corke, P.: Multirotor aerial vehicles: modeling, estimation, and control of quadrotor. IEEE Robotics & Autom. Magaz. 19, 20\u201332 (2012)","journal-title":"IEEE Robotics & Autom. Magaz."},{"key":"7632_CR22","unstructured":"Oriolo, G., Sciavicco, L., Siciliano, B., Villani, L.: Robotics: Modelling, Planning and Control (Springer, 2010)"},{"key":"7632_CR23","unstructured":"Henson, M., Seborg, D. E.: Nonlinear Process Control (Prentice Hall PTR, 1997)"},{"key":"7632_CR24","doi-asserted-by":"crossref","unstructured":"Isidori, A.: Nonlinear Control Systems (Springer Verlag, 1995)","DOI":"10.1007\/978-1-84628-615-5"},{"key":"7632_CR25","doi-asserted-by":"crossref","unstructured":"Sontag, E. D.: In Nonlinear and Optimal Control Theory 163-220 (Springer, 2008)","DOI":"10.1007\/978-3-540-77653-6_3"},{"key":"7632_CR26","doi-asserted-by":"crossref","unstructured":"Sontag, E. D.: Remarks on Stabilization and Input to-State Stability. In: Proceedings of the 28th IEEE Conference on Decision and Control 2, 1376-1378 (1989)","DOI":"10.1109\/CDC.1989.70365"},{"key":"7632_CR27","volume-title":"Linear and Nonlinear Control of UAVs: Design and Experimental Validation MA thesis","author":"L Martins","year":"2019","unstructured":"Martins, L.: Linear and Nonlinear Control of UAVs: Design and Experimental Validation MA thesis. Instituto Superior T\u00e9cnico, Lisbon, Portugal (2019)"},{"key":"7632_CR28","unstructured":"Smeur, E., H\u00f6ppener, D., De Wagter, C.: Prioritized Control Allocation for Quadrotors Subject to Saturation in (2017)"},{"key":"7632_CR29","unstructured":"Lee, D.: AR.Drone 2.0 Support from Embedded Coder (2016) http:\/\/www.mathworks.com\/hardware-support\/ar-drone.html"},{"key":"7632_CR30","doi-asserted-by":"crossref","unstructured":"Madeiras, J., Cardeira, C., Oliveira, P.: Complementary Filter Vision-Aided for Attitude and Position Estimation: Design, Analysis and Experimental Validation. In: Proceedings of the 21st IFAC Symposium on Automatic Control in Aerospace (2019)","DOI":"10.1016\/j.ifacol.2019.11.274"}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-022-07632-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11071-022-07632-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-022-07632-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T18:10:04Z","timestamp":1661969404000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11071-022-07632-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,29]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["7632"],"URL":"https:\/\/doi.org\/10.1007\/s11071-022-07632-y","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"value":"0924-090X","type":"print"},{"value":"1573-269X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,29]]},"assertion":[{"value":"16 September 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}