{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T15:53:21Z","timestamp":1783526001054,"version":"3.55.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004351","name":"Sultan Qaboos University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004351","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2017-06958"],"award-info":[{"award-number":["RGPIN-2017-06958"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013199","name":"Ministry of Economic Development and Trade, Government of Alberta","doi-asserted-by":"publisher","award":["RCP-19-001-MIF"],"award-info":[{"award-number":["RCP-19-001-MIF"]}],"id":[{"id":"10.13039\/100013199","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Intell Robot Syst"],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s10846-023-01904-4","type":"journal-article","created":{"date-parts":[[2023,8,10]],"date-time":"2023-08-10T09:02:19Z","timestamp":1691658139000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Output Tracking Dynamic Feedback Linearization of a Multirotor Suspended Load System with Disturbance Robustness"],"prefix":"10.1007","volume":"108","author":[{"given":"Mohamed","family":"Al Lawati","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zifei","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0939-534X","authenticated-orcid":false,"given":"Alan F.","family":"Lynch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,8,10]]},"reference":[{"issue":"2","key":"1904_CR1","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s10846-019-01088-w","volume":"98","author":"D Villa","year":"2020","unstructured":"Villa, D., Brandao, A., Sarcinelli-Filho, M.: A survey on load transportation using multirotor uavs. Journal of Intelligent & Robotic Systems 98(2), 267\u2013296 (2020). https:\/\/doi.org\/10.1007\/s10846-019-01088-w","journal-title":"Journal of Intelligent & Robotic Systems"},{"key":"1904_CR2","doi-asserted-by":"crossref","unstructured":"Lindsey, Q., Mellinger, D., Kumar, V.: Construction of cubic structures with quadrotor teams, pp. 177\u2013184. MIT Press (2011)","DOI":"10.7551\/mitpress\/9481.003.0028"},{"key":"1904_CR3","doi-asserted-by":"publisher","unstructured":"Pounds, P., Bersak, D., Dollar, A.: Grasping from the air: Hovering capture and load stability. In: Proc. IEEE Int. Conf. on Robotics and Automation, Toronto, ON, pp. 2491\u20132498 (2011). https:\/\/doi.org\/10.1109\/icra.2011.5980314","DOI":"10.1109\/icra.2011.5980314"},{"key":"1904_CR4","doi-asserted-by":"publisher","unstructured":"Gawel, A., Kamel, M., Novkovic, T., Widauer, J., Schindler, D., von Altishofen, B.P., Siegwart, R., Nieto, J.: Aerial picking and delivery of magnetic objects with MAVs. In: Proc. IEEE Int. Conf. on Robotics and Automation, Singapore, pp. 5746\u20135752 (2017). https:\/\/doi.org\/10.1109\/icra.2017.7989675","DOI":"10.1109\/icra.2017.7989675"},{"key":"1904_CR5","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.ast.2018.10.027","volume":"84","author":"B Shirani","year":"2019","unstructured":"Shirani, B., Najafi, M., Izadi, I.: Cooperative load transportation using multiple UAVs. Aerospace Science and Technology 84, 158\u2013169 (2019). https:\/\/doi.org\/10.1016\/j.ast.2018.10.027","journal-title":"Aerospace Science and Technology"},{"issue":"2","key":"1904_CR6","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1007\/s10846-020-01195-z","volume":"100","author":"F Rossomando","year":"2020","unstructured":"Rossomando, F., Rosales, C., Gimenez, J., Salinas, L., Soria, C., Sarcinelli-Filho, M., Carelli, R.: Aerial load transportation with multiple quadrotors based on a kinematic controller and a neural SMC dynamic compensation. Journal of Intelligent & Robotic Systems 100(2), 519\u2013530 (2020). https:\/\/doi.org\/10.1007\/s10846-020-01195-z","journal-title":"Journal of Intelligent & Robotic Systems"},{"issue":"1","key":"1904_CR7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.4050\/JAHS.46.3","volume":"46","author":"D Fusato","year":"2001","unstructured":"Fusato, D., Guglieri, G., Celi, R.: Flight dynamics of an articulated rotor helicopter with an external slung load. J. Am. Helicopter Soc. 46(1), 3\u201313 (2001). https:\/\/doi.org\/10.4050\/JAHS.46.3","journal-title":"J. Am. Helicopter Soc."},{"key":"1904_CR8","doi-asserted-by":"publisher","unstructured":"Irscheid, A., Konz, M., Rudolph, J.: A flatness-based approach to the control of distributed parameter systems applied to load transportation with heavy ropes, pp. 279\u2013294. Springer (2019). https:\/\/doi.org\/10.1007\/978-3-030-21927-7_13","DOI":"10.1007\/978-3-030-21927-7_13"},{"issue":"1","key":"1904_CR9","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1109\/TAC.2014.2336451","volume":"60","author":"T Kn\u00fcppel","year":"2014","unstructured":"Kn\u00fcppel, T., Woittennek, F.: Control design for quasi-linear hyperbolic systems with an application to the heavy rope. IEEE Transactions on Automatic Control 60(1), 5\u201318 (2014). https:\/\/doi.org\/10.1109\/TAC.2014.2336451","journal-title":"IEEE Transactions on Automatic Control"},{"key":"1904_CR10","doi-asserted-by":"publisher","unstructured":"Fliess, M., L\u00e9vine, J., Martin, P., Rouchon, P.: On differentially flat nonlinear systems. In: Nonlinear Control Systems Design. IFAC Symposia Series, pp. 159\u2013163. Pergamon, Oxford (1993). https:\/\/doi.org\/10.1016\/S1474-6670(17)52275-2","DOI":"10.1016\/S1474-6670(17)52275-2"},{"issue":"1","key":"1904_CR11","doi-asserted-by":"publisher","first-page":"2792","DOI":"10.1016\/S1474-6670(17)58099-4","volume":"29","author":"RM Murray","year":"1996","unstructured":"Murray, R.M.: Trajectory generation for a towed cable system using differential flatness. IFAC Proceedings Volumes 29(1), 2792\u20132797 (1996). https:\/\/doi.org\/10.1016\/S1474-6670(17)58099-4","journal-title":"IFAC Proceedings Volumes"},{"key":"1904_CR12","doi-asserted-by":"publisher","unstructured":"Goodarzi, F.A., Lee, D., Lee, T.: Geometric stabilization of a quadrotor UAV with a payload connected by flexible cable. In: Proc. American Control Conf., Portland, OR, pp. 4923\u20134930 (2014). https:\/\/doi.org\/10.1109\/ACC.2014.6859419","DOI":"10.1109\/ACC.2014.6859419"},{"key":"1904_CR13","doi-asserted-by":"publisher","unstructured":"Kotaru, P., Wu, G., Sreenath, K.: Differential-flatness and control of quadrotor(s) with a payload suspended through flexible cable(s). In:Proc. Indian Control Conf., Kanpur, India, pp. 352\u2013357 (2018).https:\/\/doi.org\/10.1109\/indiancc.2018.8308004","DOI":"10.1109\/indiancc.2018.8308004"},{"key":"1904_CR14","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1016\/j.apm.2020.09.027","volume":"91","author":"M Guerrero-S\u00e1nchez","year":"2021","unstructured":"Guerrero-S\u00e1nchez, M., Lozano, R., Castillo, P., Hern\u00e1ndez-Gonz\u00e1lez, O., Garc\u00eda-Beltr\u00e1n, C.D., Valencia-Palomo, G.: Nonlinear control strategies for a UAV carrying a load with swing attenuation. Applied Mathematical Modelling 91, 709\u2013722 (2021). https:\/\/doi.org\/10.1016\/j.apm.2020.09.027","journal-title":"Applied Mathematical Modelling"},{"key":"1904_CR15","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1016\/j.isatra.2017.01.027","volume":"68","author":"M Guerrero","year":"2017","unstructured":"Guerrero, M., Mercado, D.A., Lozano, R., Garc\u00eda, C.D.: Swing-attenuation for a quadrotor transporting a cable suspended payload. ISA Transactions 68, 433\u2013449 (2017). https:\/\/doi.org\/10.1016\/j.isatra.2017.01.027","journal-title":"ISA Transactions"},{"key":"1904_CR16","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s10846-017-0509-6","volume":"88","author":"K Klausen","year":"2017","unstructured":"Klausen, K., Fossen, T., Johansen, T.: Nonlinear control with swing damping of a multirotor UAV with suspended load. Journal of Intelligent & Robotic Systems 88, 379\u2013394 (2017). https:\/\/doi.org\/10.1007\/s10846-017-0509-6","journal-title":"Journal of Intelligent & Robotic Systems"},{"key":"1904_CR17","doi-asserted-by":"publisher","unstructured":"Sreenath, K., Lee, T., Kumar, V.: Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In: Proc. IEEE Int. Conf. on Decision and Control, Firenze, Italy, pp. 2269\u20132274 (2013). https:\/\/doi.org\/10.1109\/cdc.2013.6760219","DOI":"10.1109\/cdc.2013.6760219"},{"key":"1904_CR18","doi-asserted-by":"publisher","unstructured":"Bernard, M., Kondak, K.: Generic slung load transportation system using small size helicopters. In: Proc. IEEE Int. Conf. on Robotics and Automation, Kobe, Japan, pp. 3258\u20133264 (2009). https:\/\/doi.org\/10.1109\/ROBOT.2009.5152382","DOI":"10.1109\/ROBOT.2009.5152382"},{"key":"1904_CR19","doi-asserted-by":"publisher","unstructured":"Sreenath, K., Michael, N., Kumar, V.: Trajectory generation and control of a quadrotor with a cable-suspended load \u2013 a differentially-flat hybrid system. In: Proc. IEEE Int. Conf. on Robotics and Automation, Karlsruhe, Germany, pp. 4888\u20134895 (2013). https:\/\/doi.org\/10.1109\/ICRA.2013.6631275","DOI":"10.1109\/ICRA.2013.6631275"},{"issue":"3","key":"1904_CR20","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1109\/TMECH.2003.816822","volume":"8","author":"Y Fang","year":"2003","unstructured":"Fang, Y., Dixon, W., Dawson, D., Zergeroglu, E.: Nonlinear coupling control laws for an underactuated overhead crane system. IEEE\/ASME Transactions on Mechatronics 8(3), 418\u2013423 (2003). https:\/\/doi.org\/10.1109\/TMECH.2003.816822","journal-title":"IEEE\/ASME Transactions on Mechatronics"},{"issue":"5","key":"1904_CR21","doi-asserted-by":"publisher","first-page":"2653","DOI":"10.1109\/TMECH.2020.3044183","volume":"26","author":"B Xian","year":"2021","unstructured":"Xian, B., Yang, S.: Robust tracking control of a quadrotor unmanned aerial vehicle-suspended payload system. IEEE\/ASME Transactions on Mechatronics 26(5), 2653\u20132663 (2021). https:\/\/doi.org\/10.1109\/TMECH.2020.3044183","journal-title":"IEEE\/ASME Transactions on Mechatronics"},{"issue":"5","key":"1904_CR22","doi-asserted-by":"publisher","first-page":"2304","DOI":"10.1109\/TMECH.2019.2930211","volume":"24","author":"G Yu","year":"2019","unstructured":"Yu, G., Cabecinhas, D., Cunha, R., Silvestre, C.: Nonlinear backstepping control of a quadrotor-slung load system. IEEE\/ASME Transactions on Mechatronics 24(5), 2304\u20132315 (2019). https:\/\/doi.org\/10.1109\/TMECH.2019.2930211","journal-title":"IEEE\/ASME Transactions on Mechatronics"},{"key":"1904_CR23","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.6306","author":"J Reis","year":"2022","unstructured":"Reis, J., Yu, G., Cabecinhas, D., Silvestre, C.: High-performance quadrotor slung load transportation with damped oscillations. International Journal of Robust and Nonlinear Control (2022). https:\/\/doi.org\/10.1002\/rnc.6306","journal-title":"International Journal of Robust and Nonlinear Control"},{"key":"1904_CR24","doi-asserted-by":"crossref","unstructured":"Akhtar, A., Saleem, S., Shan, J.: Path invariant controllers for a quadrotor with a cable-suspended payload using a global parameterization. IEEE Transactions on Control Systems Technology (2021)","DOI":"10.1109\/TCST.2021.3133693"},{"key":"1904_CR25","doi-asserted-by":"crossref","unstructured":"Akhtar, A., Saleem, S., Shan, J.: Path following of a quadrotor with a cable-suspended payload. IEEE Transactions on Industrial Electronics (2022)","DOI":"10.1109\/TIE.2022.3167130"},{"key":"1904_CR26","unstructured":"Maplesoft\u2122: Maple (2022) Accessed 13 May, 2022. https:\/\/www.maplesoft.com\/products\/maple\/"},{"key":"1904_CR27","doi-asserted-by":"publisher","unstructured":"Mohammadhasani, A., Al\u00a0Lawati, M., Jiang, Z., Lynch, A.F.: Dynamic feedback linearization of a UAV suspended load system. In: International Conference on Unmanned Aircraft Systems (ICUAS), pp. 865\u2013872 (2022). https:\/\/doi.org\/10.1109\/ICUAS54217.2022.9836223. IEEE","DOI":"10.1109\/ICUAS54217.2022.9836223"},{"issue":"11","key":"1904_CR28","doi-asserted-by":"publisher","first-page":"1065","DOI":"10.1109\/9.14420","volume":"33","author":"H Nijmeijer","year":"1988","unstructured":"Nijmeijer, H., Respondek, W.: Dynamic input-output decoupling of nonlinear control systems. Transactions on Automatic Control 33(11), 1065\u20131070 (1988). https:\/\/doi.org\/10.1109\/9.14420","journal-title":"Transactions on Automatic Control"},{"key":"1904_CR29","volume-title":"Nonlinear Systems","author":"H Khalil","year":"2002","unstructured":"Khalil, H.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (2002)","edition":"3"},{"key":"1904_CR30","volume-title":"Control of Uncertain Systems: a Linear Programming Approach","author":"MA Dahleh","year":"1995","unstructured":"Dahleh, M.A., D\u00edaz-Bobillo, I.J.: Control of Uncertain Systems: a Linear Programming Approach. Prentice Hall, Upper Saddle River, NJ (1995)"},{"key":"1904_CR31","volume-title":"Linear Robust Control","author":"M Green","year":"2012","unstructured":"Green, M., Limebeer, D.: Linear Robust Control. Prentice-Hall, Englewood Cliffs, NJ (2012)"},{"issue":"6","key":"1904_CR32","doi-asserted-by":"publisher","first-page":"1232","DOI":"10.1137\/0324074","volume":"24","author":"H Nijmeijer","year":"1986","unstructured":"Nijmeijer, H., Schumacher, J.: The regular local noninteracting control problem for nonlinear control systems. SIAM Journal on Control and Optimization 24(6), 1232\u20131245 (1986). https:\/\/doi.org\/10.1137\/0324074","journal-title":"SIAM Journal on Control and Optimization"},{"key":"1904_CR33","doi-asserted-by":"publisher","unstructured":"Roza, A., Maggiore, M.: Path following controller for a quadrotor helicopter. In: Proc. American Control Conf., Montreal, QC, pp. 4655\u20134660 (2012). https:\/\/doi.org\/10.1109\/ACC.2012.6315061","DOI":"10.1109\/ACC.2012.6315061"},{"key":"1904_CR34","unstructured":"Fischer, G.: NONLINCON: symbolic analysis and design package for nonlinear control systems. Master\u2019s thesis, Eindhoven University of Technology, Eindhoven (1994)"},{"key":"1904_CR35","doi-asserted-by":"publisher","unstructured":"Lee, T., Leok, M., McClamroch, N.H.: Geometric tracking control of a quadrotor UAV on SE(3). In: Proc. IEEE Int. Conf. on Decision and Control, Atlanta, GA, pp. 5420\u20135425 (2010). https:\/\/doi.org\/10.1109\/CDC.2010.5717652","DOI":"10.1109\/CDC.2010.5717652"},{"issue":"1","key":"1904_CR36","doi-asserted-by":"publisher","first-page":"8189","DOI":"10.1016\/j.ifacol.2017.08.1267","volume":"50","author":"J-M Kai","year":"2017","unstructured":"Kai, J.-M., Allibert, G., Hua, M.-D., Hamel, T.: Nonlinear feedback control of quadrotors exploiting first-order drag effects. IFAC-PapersOnLine 50(1), 8189\u20138195 (2017). https:\/\/doi.org\/10.1016\/j.ifacol.2017.08.1267","journal-title":"IFAC-PapersOnLine"},{"key":"1904_CR37","doi-asserted-by":"publisher","unstructured":"Furrer, F., Burri, M., Achtelik, M., Siegwart, R.: RotorS - a modular Gazebo MAV simulator framework. Robot Operating System (ROS) The Complete Reference (Volume 1), 595\u2013625 (2016).https:\/\/doi.org\/10.1007\/978-3-319-26054-9_23","DOI":"10.1007\/978-3-319-26054-9_23"},{"key":"1904_CR38","unstructured":"PX4 Gazebo Simulation (2023). https:\/\/docs.px4.io\/main\/en\/sim_gazebo_gz\/. Accessed: 28 April 2023"},{"key":"1904_CR39","doi-asserted-by":"crossref","unstructured":"Jiang, Z., Al\u00a0Lawati, M., Mohammadhasani, A., Lynch, A.: Quasi-static state feedback output tracking for a slung load system : PX4 SITL validation (under review). Journal of Intelligent & Robotic Systems (2023)","DOI":"10.1109\/AIM46323.2023.10196275"},{"key":"1904_CR40","doi-asserted-by":"publisher","unstructured":"Omari, S., Hua, M.-D., Ducard, G., Hamel, T.: Nonlinear control of VTOL UAVs incorporating flapping dynamics. In: IEEE\/RSJ International Conference on Intelligent Robots and Systems, pp. 2419\u20132425 (2013). https:\/\/doi.org\/10.1109\/IROS.2013.6696696. IEEE","DOI":"10.1109\/IROS.2013.6696696"}],"container-title":["Journal of Intelligent & Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-023-01904-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10846-023-01904-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10846-023-01904-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T01:06:39Z","timestamp":1693530399000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10846-023-01904-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8]]},"references-count":40,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["1904"],"URL":"https:\/\/doi.org\/10.1007\/s10846-023-01904-4","relation":{},"ISSN":["0921-0296","1573-0409"],"issn-type":[{"value":"0921-0296","type":"print"},{"value":"1573-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8]]},"assertion":[{"value":"2 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 August 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Statements and Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}},{"value":"The research does not involve human participants, their data or biological material and it does not involve animals.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not applicable.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"82"}}