{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T10:47:53Z","timestamp":1781779673369,"version":"3.54.5"},"reference-count":91,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T00:00:00Z","timestamp":1699315200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"name":"Hong Kong RGC ECS","award":["27202219"],"award-info":[{"award-number":["27202219"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:p>We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate (not simplified) aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints, and actuator saturation. The planned trajectory of flat output is transformed into state trajectory in real time with optional consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The proposed algorithms are implemented on our quadrotor tail-sitter prototype, \u201cHong Hu,\u201d and their effectiveness are demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10\u00a0m\/s, typical tail-sitter maneuvers (transition, level flight, and loiter) with speed up to 20\u00a0m\/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight, and Cuban Eight) with acceleration up to 2.5\u00a0 g. The video demonstration is available at https:\/\/youtu.be\/2x_bLbVuyrk .<\/jats:p>","DOI":"10.1177\/02783649231207655","type":"journal-article","created":{"date-parts":[[2023,11,8]],"date-time":"2023-11-08T01:33:35Z","timestamp":1699407215000},"page":"241-280","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":34,"title":["Trajectory generation and tracking control for aggressive tail-sitter flights"],"prefix":"10.1177","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4977-0423","authenticated-orcid":false,"given":"Guozheng","family":"Lu","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, The University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0321-1164","authenticated-orcid":false,"given":"Yixi","family":"Cai","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, The University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1359-7235","authenticated-orcid":false,"given":"Nan","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, The University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fanze","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, The University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5392-8924","authenticated-orcid":false,"given":"Yunfan","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, The University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, The University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2023,11,7]]},"reference":[{"key":"bibr1-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2015.7353624"},{"key":"bibr2-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1177\/1756829320914264"},{"key":"bibr3-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1017\/9781139061759"},{"key":"bibr4-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/6.2011-1255"},{"key":"bibr5-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1177\/0278364914558129"},{"key":"bibr6-02783649231207655","volume-title":"Proportional Derivative (Pd) Control on the Euclidean Group","author":"Bullo F","year":"1995"},{"key":"bibr7-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/6.2014-0016"},{"issue":"5","key":"bibr8-02783649231207655","first-page":"733","volume":"19","author":"\u00c7etinsoy E","year":"2011","journal-title":"Turkish Journal of Electrical Engineering and Computer Sciences"},{"key":"bibr9-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2022.3145087"},{"key":"bibr10-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2007.4434966"},{"key":"bibr11-02783649231207655","volume-title":"Aerodynamics","author":"Clancy LJ","year":"1975"},{"key":"bibr12-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1002\/rob.21789"},{"key":"bibr13-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2019.2926390"},{"key":"bibr14-02783649231207655","volume-title":"Dynamics of Flight","author":"Etkin B","year":"1959"},{"key":"bibr15-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2017.2776353"},{"key":"bibr16-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2017.7989679"},{"key":"bibr17-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2018.8593739"},{"key":"bibr18-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1080\/00207179508921959"},{"key":"bibr19-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1126\/scirobotics.abh1221"},{"key":"bibr20-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/6.2007-6318"},{"key":"bibr21-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1002\/rob.21842"},{"key":"bibr22-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1145\/641876.641880"},{"key":"bibr23-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/CCTA.2017.8062443"},{"key":"bibr24-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144504446096"},{"key":"bibr25-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICUAS.2017.7991420"},{"key":"bibr26-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICUAS.2018.8453458"},{"key":"bibr27-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1126\/scirobotics.aau6637"},{"key":"bibr28-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(92)90029-F"},{"key":"bibr29-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2011.08.003"},{"key":"bibr30-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICUAS.2015.7152330"},{"key":"bibr31-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-011-9585-1"},{"key":"bibr32-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2017.08.849"},{"key":"bibr33-02783649231207655","doi-asserted-by":"publisher","DOI":"10.15607\/RSS.2020.XVI.040"},{"key":"bibr34-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1163\/016918610X493570"},{"key":"bibr35-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/6.1983-2239"},{"key":"bibr36-02783649231207655","doi-asserted-by":"publisher","DOI":"10.3390\/s18092859"},{"key":"bibr37-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TMECH.2020.2983255"},{"key":"bibr38-02783649231207655","doi-asserted-by":"crossref","unstructured":"Li Y, Qin Y, Xu W, et al. (2020b) Modeling, identification, and control of non-minimum phase dynamics of bi-copter uavs. 2020 IEEE\/ASME international conference on advanced intelligent mechatronics (AIM), Boston, MA, USA, 6\u20139 July 2020.","DOI":"10.1109\/AIM43001.2020.9158910"},{"key":"bibr39-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2017.2663526"},{"key":"bibr40-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2022.3212397"},{"key":"bibr41-02783649231207655","volume-title":"The Phi-Theory Approach to Flight Control Design of Hybrid Vehicles","author":"Lustosa LR","year":"2017"},{"key":"bibr42-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/1.G003374"},{"key":"bibr43-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2017.7989452"},{"key":"bibr44-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2017.8206400"},{"key":"bibr45-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1177\/1756829318813633"},{"key":"bibr46-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2018.2847405"},{"key":"bibr47-02783649231207655","volume-title":"Flipping the script with atlas","author":"Marion P","year":"2021"},{"key":"bibr48-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(95)00099-2"},{"key":"bibr49-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.2010.5509183"},{"key":"bibr50-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(99)00214-9"},{"key":"bibr51-02783649231207655","doi-asserted-by":"publisher","DOI":"10.4050\/F-0078-2022-17639"},{"key":"bibr52-02783649231207655","volume-title":"One Step beyond, Rotor Wing","author":"McKenna J","year":"2007"},{"key":"bibr53-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2015.7140074"},{"key":"bibr54-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2011.5980409"},{"key":"bibr55-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1177\/0278364911434236"},{"key":"bibr56-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2015.2479878"},{"key":"bibr57-02783649231207655","unstructured":"Murray RM, Rathinam M, Sluis W (1995) Differential flatness of mechanical control systems: a catalog of prototype systems. ASME international mechanical engineering congress and exposition, Columbus, OH, USA, 30 October 1995."},{"key":"bibr58-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2011.01.027"},{"key":"bibr59-02783649231207655","doi-asserted-by":"publisher","DOI":"10.23919\/ECC54610.2021.9654841"},{"key":"bibr60-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymssp.2019.106358"},{"key":"bibr61-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2013.6630594"},{"key":"bibr62-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-016-9599-4"},{"key":"bibr63-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-013-9900-0"},{"key":"bibr64-02783649231207655","volume-title":"Arcturus Uav Upgrades the Jump15 Vtol Uav. Airlines & Aviation","author":"Park R","year":"2014"},{"key":"bibr65-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/6.2004-4900"},{"key":"bibr66-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2012.6315035"},{"key":"bibr67-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2013.6760648"},{"key":"bibr68-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA48891.2023.10160767"},{"key":"bibr69-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2017.7989318"},{"key":"bibr70-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2022.3185772"},{"key":"bibr71-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1177\/0278364914528132"},{"key":"bibr72-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2011.5980357"},{"key":"bibr73-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/1.G004520"},{"key":"bibr74-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1002\/9781119174882"},{"key":"bibr75-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechatronics.2018.10.001"},{"key":"bibr76-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2022.3177279"},{"key":"bibr77-02783649231207655","doi-asserted-by":"crossref","unstructured":"Tal EA, Karaman S (2021) Global trajectory-tracking control for a tailsitter flying wing in agile uncoordinated flight. AIAA aviation 2021 forum, Reston, VA, 2\u20136 August 2021.","DOI":"10.2514\/6.2021-3214"},{"key":"bibr78-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/1.G006645"},{"key":"bibr79-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2023.3301312"},{"key":"bibr80-02783649231207655","doi-asserted-by":"publisher","DOI":"10.2514\/2.4202"},{"key":"bibr81-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICRA.2016.7487466"},{"key":"bibr82-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1002\/aisy.202200297"},{"key":"bibr83-02783649231207655","doi-asserted-by":"crossref","unstructured":"Wang K, Ke Y, Lai S, et al. (2017a) Model-based optimal auto-transition and control synthesis for tail-sitter uav kh-lion. 2017 13th IEEE international conference on control & automation (ICCA), Ohrid, Macedonia, 3\u20136 July 2017.","DOI":"10.1109\/ICCA.2017.8003118"},{"key":"bibr84-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2017.8206492"},{"key":"bibr85-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2022.3160022"},{"key":"bibr86-02783649231207655","doi-asserted-by":"crossref","unstructured":"Xu W, Gu H, Qing Y, et al. (2019a) Full attitude control of an efficient quadrotor tail-sitter vtol uav with flexible modes. 2019 international conference on unmanned aircraft systems (ICUAS), Atlanta, GA, USA, 11-14 June 2019.","DOI":"10.1109\/ICUAS.2019.8797947"},{"key":"bibr87-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1186\/s40360-019-0288-8"},{"key":"bibr88-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1002\/rob.21952"},{"key":"bibr89-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2017.8206359"},{"key":"bibr90-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/ICUAS.2018.8453475"},{"key":"bibr91-02783649231207655","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2019.2927938"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649231207655","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/02783649231207655","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783649231207655","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:17:12Z","timestamp":1777457832000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783649231207655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,7]]},"references-count":91,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["10.1177\/02783649231207655"],"URL":"https:\/\/doi.org\/10.1177\/02783649231207655","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,7]]}}}