[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86288-en":3,"doc-seo-86288-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86288,1099514068365,"Aurelia","https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068",8,"Research & Report","Coordinated Incremental Trajectory Tracking of a Tailsitter Drone","Analytical differential flatness transform is derived for a tailsitter UAV operating under coordinated flight conditions, using a simplified aerodynamic model. The framework is built solely on rotation matrices to eliminate Euler-angle ambiguities. It extends an existing differential-flatness-based controller to regimes with substantial vertical velocity, where earlier methods fail. Experimental validation uses trajectories that demonstrate improved applicability and well-defined behavior in these regimes, highlighting the controller’s limits and strengths.","Coordinated Incremental Trajectory Tracking of a Tailsitter Drone  \nEvangelos Ntouros∗ and Ewoud J. J. Smeur  \narXiv :2607 . 11651v1 [ cs .RO] 13 Jul 2026  \nAbstract—This paper derives an analytical differential flatness transform for a tailsitter Unmanned Aerial Vehicle (UAV) under coordinated flight conditions using a simplified aerodynamic model. The proposed framework is formulated exclusively using rotation matrices, avoiding the ambiguities inherent to Euler angle representations. The method extends the applicability of an existing state-of-the-art differential flatnessbased controller to flight regimes involving a significant vertical velocity component, where the previous approach becomes inapplicable. The proposed framework is validated experimentally with trajectories that highlight its advantages in these regimes.  \nI. INTRODUCTION  \nHybrid Unmanned Aerial Vehicles (UAVs) combine the hover capability of rotorcraft with the higher cruise speed and aerodynamic efficiency of fixed-wing aircraft. A specific subclass is the tailsitter UAV, which transitions from hover to forward flight by pitching down approximately 90◦ . Typical tailsitter configurations include the dual-motor tailsitter, equipped with two non-tilting propellers and two elevons [1], and the quadrotor tailsitter, which integrates aquadrotor configuration with a lifting wing [2] . Due to their simplicity, tailsitters have attracted considerable attention in recent years for applications such as search and rescue, mapping, and package delivery. However, controlling these vehicles remains challenging as they combine coordinated and uncoordinated flight and can operate across a wide flight envelope including the post-stall regime during transition flight.  \nTal et al. [3] employed a dynamic model of a dual-motor tailsitter based on the ϕ-theory parameterization proposed in [4] . This formulation enabled them to prove the differential flatness property of the platform for uncoordinated flight. Leveraging this property, they computed feedforward angular rate signals and integrated them within the incremental control architecture of [5], demonstrating agile uncoordinated flight. Although coordinated flight was also considered, the presented results relied on assumptions valid only for level flight and therefore do not directly extend to trajectories with a significant vertical velocity component.  \nTo address coordinated flight with vertical velocity component, authors in [6] demonstrated the differential flatness property of a quadrotor tailsitter for coordinated flight conditions. Their approach relies on the standard Buckingham  \nThis work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.  \nAll authors are with Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands.  \n∗ Corresponding [author](author e.ntouros@tudelft.nl)[ e.ntouros@tudelft.nl](author e.ntouros@tudelft.nl)  \nπ-theory aerodynamic model identified from wind-tunnel experiments. While this formulation captures a broader range of aerodynamic effects, it requires a costly and time consuming identification process. Moreover, it introduces singularities around hover where the angle of attack and the sideslip angle are not defined. Furthermore, as shown in [6], the differential flatness transform cannot be obtained in closed form and must instead be derived numerically, due to the increased complexity of the underlying aerodynamic model.  \nResearchers in [7] employed the simplified aerodynamic model of [8] and derived an analytical differential flatness transform for the coordinated flight of quadcopter tailsitters with arbitrary wing installation angles. While extending the applicability to generic platform configurations, the formulation remains based on the angle of attack and the demonstrated results are limited to level flight.  \nThe contribution of this work is the","cbCaicKWEQ0WyPUt","https://ap.wps.com/l/cbCaicKWEQ0WyPUt","pdf",2101997,4,1,6,"English","en",105,"# Introduction\n# Tailsitter Model\n## Target vehicle and reference frames\n## Coordinated flight challenges\n# Proposed analytical flatness transform\n## Rotation-matrix formulation\n# Experimental validation\n## Trajectories with significant vertical velocity","[{\"question\":\"What is the main contribution of the paper for tailsitter drones?\",\"answer\":\"The paper derives an analytical differential flatness transform for a tailsitter aircraft in coordinated flight, enabling incremental trajectory tracking beyond regimes with small vertical velocity components.\"},{\"question\":\"Why does the method avoid Euler angles?\",\"answer\":\"The formulation uses rotation matrices exclusively, avoiding ambiguities and singularities that arise from Euler-angle representations.\"},{\"question\":\"How is the approach validated and what do experiments show?\",\"answer\":\"Experiments test trajectories with significant vertical velocity components, showing where the prior method becomes unsuitable and produces singularities, while the proposed transform remains well-defined.\"}]",1784210101,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"coordinated-incremental-trajectory-tracking-of-a-tailsitter-drone","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/coordinated-incremental-trajectory-tracking-of-a-tailsitter-drone/86288/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main contribution of the paper for tailsitter drones?","Question",{"text":75,"@type":76},"The paper derives an analytical differential flatness transform for a tailsitter aircraft in coordinated flight, enabling incremental trajectory tracking beyond regimes with small vertical velocity components.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why does the method avoid Euler angles?",{"text":80,"@type":76},"The formulation uses rotation matrices exclusively, avoiding ambiguities and singularities that arise from Euler-angle representations.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the approach validated and what do experiments show?",{"text":84,"@type":76},"Experiments test trajectories with significant vertical velocity components, showing where the prior method becomes unsuitable and produces singularities, while the proposed transform remains 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