{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T03:25:38Z","timestamp":1765423538160,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T00:00:00Z","timestamp":1718582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Funds by FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["10.54499\/UIDB\/50022\/2020","10.54499\/PCIF\/SSI\/0103\/2018"],"award-info":[{"award-number":["10.54499\/UIDB\/50022\/2020","10.54499\/PCIF\/SSI\/0103\/2018"]}]},{"name":"LAETA Base Funding","award":["10.54499\/UIDB\/50022\/2020","10.54499\/PCIF\/SSI\/0103\/2018"],"award-info":[{"award-number":["10.54499\/UIDB\/50022\/2020","10.54499\/PCIF\/SSI\/0103\/2018"]}]},{"name":"Eye in the Sky","award":["10.54499\/UIDB\/50022\/2020","10.54499\/PCIF\/SSI\/0103\/2018"],"award-info":[{"award-number":["10.54499\/UIDB\/50022\/2020","10.54499\/PCIF\/SSI\/0103\/2018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Actuators"],"abstract":"<jats:p>Incremental control strategies such as Incremental Nonlinear Dynamics Inversion (INDI) and Incremental Backstepping (IBKS) provide undeniable advantages for controlling Uncrewed Aerial Vehicles (UAVs) due to their reduced model dependency and accurate tracking capacities, which is of particular relevance for tail-sitters as these perform complex, hard to model manoeuvres when transitioning to and from aerodynamic flight. In this research article, a quaternion-based form of IBKS is originally deduced and applied to the stabilization of a tail-sitter in vertical flight, which is then implemented in a flight controller and validated in a Hardware-in-the-Loop simulation, which is also made for the INDI controller. Experimental validation with indoor flight tests of both INDI and IBKS controllers follows, evaluating their performance in stabilizing the tail-sitter prototype in vertical flight. Lastly, the tracking results obtained from the experimental trials are analysed, allowing an objective comparison to be drawn between these controllers, evaluating their respective advantages and limitations. From the successfully conducted flight tests, it was found that both incremental solutions are suited to control a tail-sitter in vertical flight, providing accurate tracking capabilities with smooth actuation, and only requiring the actuation model. Furthermore, it was found that the IBKS is significantly more computationally demanding than the INDI, although having a global proof of stability that is of interest in aircraft control.<\/jats:p>","DOI":"10.3390\/act13060225","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T06:29:43Z","timestamp":1718605783000},"page":"225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Incremental Nonlinear Dynamics Inversion and Incremental Backstepping: Experimental Attitude Control of a Tail-Sitter UAV"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5424-5033","authenticated-orcid":false,"given":"Alexandre","family":"Athayde","sequence":"first","affiliation":[{"name":"IDMEC\u2014Instituto de Engenharia Mec\u00e2nica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4271-7996","authenticated-orcid":false,"given":"Alexandra","family":"Moutinho","sequence":"additional","affiliation":[{"name":"IDMEC\u2014Instituto de Engenharia Mec\u00e2nica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0759-3211","authenticated-orcid":false,"given":"Jos\u00e9 Raul","family":"Azinheira","sequence":"additional","affiliation":[{"name":"IDMEC\u2014Instituto de Engenharia Mec\u00e2nica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1016\/j.comcom.2019.10.016","article-title":"An evaluative review of the VTOL technologies for unmanned and manned aerial vehicles","volume":"149","author":"Zhou","year":"2020","journal-title":"Comput. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Rakesh, D., Kumar, N.A., Sivaguru, M., Keerthivaasan, K.V.R., Janaki, B.R., and Raffik, R. (2021, January 8\u20139). Role of UAVs in innovating agriculture with future applications: A review. Proceedings of the 2021 International Conference on Advancements in Electrical, Electronics, Communication, Computing and Automation (ICAECA), Coimbatore, India.","DOI":"10.1109\/ICAECA52838.2021.9675612"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107035","DOI":"10.1016\/j.ast.2021.107035","article-title":"Review of designs and flight control techniques of hybrid and convertible VTOL UAVs","volume":"118","author":"Ducard","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.paerosci.2018.03.007","article-title":"A survey of hybrid unmanned aerial vehicles","volume":"98","author":"Saeed","year":"2018","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.23919\/JSEE.2021.000090","article-title":"PID-type fault-tolerant prescribed performance control of fixed-wing UAV","volume":"32","author":"Yu","year":"2021","journal-title":"J. Syst. Eng. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kazemi, M.H., and Tarighi, R. (2024). PID-based attitude control of quadrotor using robust pole assignment and LPV modeling. Int. J. Dyn. Control.","DOI":"10.1007\/s40435-023-01372-6"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Tunik, A.A., and Nadsadna, O.I. (2017, January 17\u201319). Robust digital gain-scheduling control of the UAV altitude. Proceedings of the 2017 IEEE 4th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD), Kiev, Ukraine.","DOI":"10.1109\/APUAVD.2017.8308803"},{"key":"ref_8","unstructured":"Wang, J., Holzapfel, F., and Peter, F. (2013, January 10\u201312). Comparison of nonlinear dynamic inversion and backstepping controls with application to a quadrotor. Proceedings of the EuroGNC, Delft, The Netherlands."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1109\/TCST.2007.908209","article-title":"Hover Control of an UAV with Backstepping Design Including Input Saturations","volume":"16","author":"Azinheira","year":"2014","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_10","first-page":"573","article-title":"Mitigating Time-Delay in Nonlinear Dynamics Inversion for Multirotor Unmanned Aerial Vehicles","volume":"47","author":"Jang","year":"2024","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Xin, H., Chen, Q., Xian, Y., Wang, P., Wang, Y., Yao, X., and Hou, Z. (2024). Longitudinal Decoupling Control of Altitude and Velocity for a Fixed-Wing Aircraft. IEEE Trans. Intell. Veh., early access.","DOI":"10.1109\/TIV.2024.3388257"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Khanna, A., and Mukherjee, B.K. (2023, January 1\u20133). UAV Performing Level Turn Maneuver Under CG Offset: Backstepping Control Scheme. Proceedings of the 10th IEEE Uttar Pradesh Section International Conference on Electrical, Electronics and Computer Engineering (UPCON), Gautam Buddha Nagar, India.","DOI":"10.1109\/UPCON59197.2023.10434705"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Lombaerts, T., Kaneshige, J., Schuet, S., Hardy, G., Aponso, B.L., and Shish, K.H. (2019, January 7\u201311). Nonlinear dynamic inversion based attitude control for a hovering quad tiltrotor eVTOL vehicle. Proceedings of the AIAA Scitech 2019 Forum, San Diego, CA, USA.","DOI":"10.2514\/6.2019-0134"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s10846-012-9744-z","article-title":"Integral backstepping control of an unconventional dual-fan unmanned aerial vehicle","volume":"69","author":"Amiri","year":"2013","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3492","DOI":"10.1109\/TAES.2021.3082663","article-title":"Robustness of incremental backstepping flight controllers: The boeing 747 case study","volume":"57","author":"Cordeiro","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Safwat, E., Weiguo, Z., Kassem, M., and Mohsen, A. (2020, January 6\u201310). Robust Nonlinear Flight Controller For Small Unmanned Aircraft Vehicle based on Incremental BackStepping. Proceedings of the AIAA Scitech 2020 Forum, Orlando, FL, USA.","DOI":"10.2514\/6.2020-0854"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"954","DOI":"10.2514\/1.G003001","article-title":"Command-filtered incremental backstepping controller for small unmanned aerial vehicles","volume":"41","author":"Wang","year":"2018","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1109\/TCST.2020.3001117","article-title":"Accurate tracking of aggressive quadrotor trajectories using incremental nonlinear dynamic inversion and differential flatness","volume":"29","author":"Tal","year":"2020","journal-title":"IEEE Trans. Control. Syst. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"274","DOI":"10.2514\/1.G004520","article-title":"Incremental control and guidance of hybrid aircraft applied to a tailsitter unmanned air vehicle","volume":"43","author":"Smeur","year":"2020","journal-title":"J. Guid. Control. Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Tal, E.A., and Karaman, S. (2021, January 2\u20136). Global trajectory-tracking control for a tailsitter flying wing in agile uncoordinated flight. Proceedings of the AIAA Aviation 2021 Forum, Virtual Event.","DOI":"10.2514\/6.2021-3214"},{"key":"ref_21","unstructured":"Beard, R.W., and McLain, T.W. (2018). Small Unmanned Aircraft: Theory and Practice, Princeton University Press. [1st ed.]."},{"key":"ref_22","unstructured":"(2024, April 16). E-Flite XVERT VTOL Webpage. Available online: https:\/\/www.horizonhobby.de\/en_DE\/product\/x-vert-vtol-bnf-basic-504mm\/EFL1850.html."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Athayde, A., Moutinho, A., and Azinheira, J.R. (2024). Experimental Nonlinear and Incremental Control Stabilization of a Tail-Sitter UAV with Hardware-in-the-Loop Validation. Robotics, 13.","DOI":"10.20944\/preprints202402.0467.v1"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chiappinelli, R., and Nahon, M. (2018, January 12\u201315). Modeling and Control of a Tailsitter UAV. Proceedings of the 2018 International Conference on Unmanned Aircraft Systems (ICUAS), Dallas, TX, USA.","DOI":"10.1109\/ICUAS.2018.8453301"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Stevens, B.L., and Lewis, F.L. (2016). Aircraft Control and Simulation: Dynamics, Controls Design, and Autonomous Systems, John Wiley & Sons. [3rd ed.].","DOI":"10.1002\/9781119174882"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Khan, W., and Nahon, M. (2015, January 9\u201312). Real-time modeling of agile fixed-wing UAV aerodynamics. Proceedings of the 2015 International Conference on Unmanned Aircraft Systems (ICUAS), Denver, CO, USA.","DOI":"10.1109\/ICUAS.2015.7152411"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Khan, W., and Nahon, M. (2016, January 7\u201310). Modeling dynamics of agile fixed-wing UAVs for real-time applications. Proceedings of the 2016 International Conference on Unmanned Aircraft Systems (ICUAS), Arlington, VA, USA.","DOI":"10.1109\/ICUAS.2016.7502599"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1109\/TMECH.2013.2264105","article-title":"Toward an accurate physics-based UAV thruster model","volume":"18","author":"Khan","year":"2013","journal-title":"IEEE ASME Trans. Mechatron."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Madgwick, S.O., Harrison, A.J., and Vaidyanathan, R. (July, January 29). Estimation of IMU and MARG orientation using a gradient descent algorithm. Proceedings of the 2011 IEEE International Conference on Rehabilitation Robotics, Zurich, Switzerland.","DOI":"10.1109\/ICORR.2011.5975346"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Horn, J.F. (2019). Non-linear dynamic inversion control design for rotorcraft. Aerospace, 6.","DOI":"10.3390\/aerospace6030038"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Coelho, R., Moutinho, A., and Azinheira, J.R. (2017, January 26\u201328). Quadrotor Attitude Control using Incremental Nonlinear Dynamics Inversion. Proceedings of the International Conference on Informatics in Control, Automation and Robotics, Madrid, Spain.","DOI":"10.5220\/0006435900980109"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.ifacol.2015.12.012","article-title":"Lateral control of airship with uncertain dynamics using incremental nonlinear dynamics inversion","volume":"48","author":"Azinheira","year":"2015","journal-title":"IFAC Pap. Online"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1109\/TAES.2021.3123215","article-title":"Increased robustness to delay in incremental controllers using input scaling gain","volume":"58","author":"Cordeiro","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_34","unstructured":"Acquatella, P., van Kampen, E., and Chu, Q.P. (2013, January 10\u201312). Incremental backstepping for robust nonlinear flight control. Proceedings of the EuroGNC 2013, Delft, The Netherlands."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Oland, E., and Kristiansen, R. (2013, January 2\u20139). Quaternion-based backstepping control of a fixed-wing unmanned aerial vehicle. Proceedings of the IEEE Aerospace Conference, Big Sky, MT, USA.","DOI":"10.1109\/AERO.2013.6497180"},{"key":"ref_36","unstructured":"Khalil, H.K. (2020). Nonlinear Systems, Prentice Hall. [3rd ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Van Ekeren, W., Looye, G., Kuchar, R., Chu, Q., and Van Kampen, E.J. (2018, January 8\u201312). Design, implementation and flight-test of incremental backstepping flight control laws. Proceedings of the AIAA Guidance, Navigation, and Control Conference, Kissimmee, FL, USA.","DOI":"10.2514\/6.2018-0384"},{"key":"ref_38","unstructured":"(2024, April 16). Arduino Nano 33 IOT Product Page. Available online: https:\/\/docs.arduino.cc\/hardware\/nano-33-iot\/."},{"key":"ref_39","unstructured":"(2024, April 16). Wiznet W5500 Product Page. Available online: https:\/\/www.wiznet.io\/product-item\/w5500\/."},{"key":"ref_40","unstructured":"(2024, April 16). Basic Linear Algebra Library Page, by Tom Stewart. Available online: https:\/\/github.com\/tomstewart89\/BasicLinearAlgebra."},{"key":"ref_41","unstructured":"(2024, April 16). Nordic Semiconductor nRF24 Series Product Page. Available online: https:\/\/www.nordicsemi.com\/Products\/nRF24-series."},{"key":"ref_42","unstructured":"(2024, April 16). NRF24L01 Library Page, by TMRh20. Available online: https:\/\/nrf24.github.io\/RF24\/."},{"key":"ref_43","unstructured":"(2024, April 16). MS5611 Barometer Product Page. Available online: https:\/\/www.okystar.com\/product-item\/gy-63-ms5611-atmospheric-pressure-sensor-module-height-sensor-module-iicspi-communication-oky3232\/29\/."},{"key":"ref_44","unstructured":"(2024, April 16). MS5611 Pressure and Temperature Sensor Library Page, by Rob Tillaart. Available online: https:\/\/www.arduino.cc\/reference\/en\/libraries\/ms5611\/."},{"key":"ref_45","unstructured":"(2024, April 16). Raspberry Pi Pico Product Page. Available online: https:\/\/www.raspberrypi.com\/documentation\/microcontrollers\/raspberry-pi-pico.html."},{"key":"ref_46","unstructured":"(2024, April 16). Raspberry Pi Pico Arduino Core Page, by Earle F. Philhower, III. Available online: https:\/\/arduino-pico.readthedocs.io\/en\/latest\/."}],"container-title":["Actuators"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-0825\/13\/6\/225\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:59:54Z","timestamp":1760108394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-0825\/13\/6\/225"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,17]]},"references-count":46,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["act13060225"],"URL":"https:\/\/doi.org\/10.3390\/act13060225","relation":{},"ISSN":["2076-0825"],"issn-type":[{"type":"electronic","value":"2076-0825"}],"subject":[],"published":{"date-parts":[[2024,6,17]]}}}