{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:47:09Z","timestamp":1774450029202,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T00:00:00Z","timestamp":1643068800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper proposes a barrier function adaptive non-singular terminal sliding mode controller for a six-degrees-of-freedom (6DoF) quad-rotor in the existence of matched disturbances. For this reason, a linear sliding surface according to the tracking error dynamics is proposed for the convergence of tracking errors to origin. Afterward, a novel non-singular terminal sliding surface is suggested to guarantee the finite-time reachability of the linear sliding surface to origin. Moreover, for the rejection of the matched disturbances that enter into the quad-rotor system, an adaptive control law based on barrier function is recommended to approximate the matched disturbances at any moment. The barrier function-based control technique has two valuable properties. First, this function forces the error dynamics to converge on a region near the origin in a finite time. Secondly, it can remove the increase in the adaptive gain because of the matched disturbances. Lastly, simulation results are given to demonstrate the validation of this technique.<\/jats:p>","DOI":"10.3390\/s22030909","type":"journal-article","created":{"date-parts":[[2022,1,25]],"date-time":"2022-01-25T21:07:11Z","timestamp":1643144831000},"page":"909","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Barrier Function Adaptive Nonsingular Terminal Sliding Mode Control Approach for Quad-Rotor Unmanned Aerial Vehicles"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6528-3636","authenticated-orcid":false,"given":"Khalid A.","family":"Alattas","sequence":"first","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, College of Computer Science and Engineering, University of Jeddah, Jeddah 23890, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Omid","family":"Mofid","sequence":"additional","affiliation":[{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, Douliou 64002, Yunlin, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9221-4385","authenticated-orcid":false,"given":"Abdullah K.","family":"Alanazi","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hala M.","family":"Abo-Dief","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1271-8488","authenticated-orcid":false,"given":"Andrzej","family":"Bartoszewicz","sequence":"additional","affiliation":[{"name":"Institute of Automatic Control, Lodz University of Technology, 18\/22 Stefanowskiego St., 90-924 Lodz, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7244-2949","authenticated-orcid":false,"given":"Mohsen","family":"Bakouri","sequence":"additional","affiliation":[{"name":"Department of Medical Equipment Technology, College of Applied Medical Science, Majmaah University, Majmaah 11952, Saudi Arabia"},{"name":"Department of Physics, College of Arts, Fezzan University, Traghen 71340, Libya"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5676-1875","authenticated-orcid":false,"given":"Saleh","family":"Mobayen","sequence":"additional","affiliation":[{"name":"Future Technology Research Center, National Yunlin University of Science and Technology, Douliou 64002, Yunlin, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"062074","DOI":"10.1088\/1742-6596\/1748\/6\/062074","article-title":"Design of Sliding Mode Controller for Tilting Quadrotor UAV Based on Predetermined Performance","volume":"1748","author":"Zhou","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mehmood, Y., Aslam, J., Ullah, N., Chowdhury, M., Techato, K., and Alzaed, A.N. (2021). Adaptive Robust Trajectory Tracking Control of Multiple Quad-Rotor UAVs with Parametric Uncertainties and Disturbances. Sensors, 21.","DOI":"10.3390\/s21072401"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1109\/TMECH.2014.2352647","article-title":"Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode","volume":"20","author":"Zheng","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yuan, D., and Wang, Y. (2021). Data Driven Model-Free Adaptive Control Method for Quadrotor Formation Trajectory Tracking Based on RISE and ISMC Algorithm. Sensors, 21.","DOI":"10.3390\/s21041289"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.2514\/1.J058327","article-title":"Quad-rotor flight simulation in realistic atmospheric conditions","volume":"58","author":"Davoudi","year":"2020","journal-title":"AIAA J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1109\/TCYB.2020.2969281","article-title":"Fully adaptive-gain-based intelligent failure-tolerant control for spacecraft attitude stabilization under actuator saturation","volume":"52","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Cybern."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Nakamura, S., Higashi, Y., Masuda, A., and Miura, N. (2020, January 12\u201315). A Positioning System and Position Control System of a Quad-Rotor Applying Kalman Filter to a UWB Module and an IMU. Proceedings of the 2020 IEEE\/SICE International Symposium on System Integration (SII), Honolulu, HI, USA.","DOI":"10.1109\/SII46433.2020.9025894"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Machini Malachias Marques, F., Augusto Queiroz Assis, P., and Mendes Finzi Neto, R. (2020, January 8). Position Tracking of a Tilt-rotor Quad-copter With Small Attitude Variation Using Model Predictive Control. Proceedings of the AIAA Aviation 2020 Forum, Virtual.","DOI":"10.2514\/6.2020-3194"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.1002\/asjc.1495","article-title":"Attitude tracking control of a quad-rotor with partial loss of rotation effectiveness","volume":"19","author":"Song","year":"2017","journal-title":"Asian J. Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2110","DOI":"10.1002\/rnc.5030","article-title":"Distributed sliding mode control for leader-follower formation flight of fixed-wing unmanned aerial vehicles subject to velocity constraints","volume":"31","author":"Wang","year":"2021","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3243","DOI":"10.1109\/TCYB.2018.2794968","article-title":"Finite-time formation control of under-actuated ships using nonlinear sliding mode control","volume":"48","author":"Li","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_12","unstructured":"Chen, H., Liu, Y.-J., Liu, L., Tong, S., and Gao, Z. (2021). Anti-Saturation-Based Adaptive Sliding-Mode Control for Active Suspension Systems With Time-Varying Vertical Displacement and Speed Constraints. IEEE Trans. Cybern., 1\u201311."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1681","DOI":"10.1109\/TCYB.2016.2555307","article-title":"Finite time fault tolerant control for robot manipulators using time delay estimation and continuous nonsingular fast terminal sliding mode control","volume":"47","author":"Van","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1109\/TCYB.2018.2818747","article-title":"Two new discrete-time neurodynamic algorithms applied to online future matrix inversion with nonsingular or sometimes-singular coefficient","volume":"49","author":"Qiu","year":"2018","journal-title":"IEEE Trans. Cybern."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1109\/TSMC.2017.2782246","article-title":"An adaptive backstepping nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators","volume":"49","author":"Van","year":"2018","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4288","DOI":"10.1109\/TAES.2020.2988836","article-title":"Fast nonsingular terminal sliding mode flight control for multirotor aerial vehicles","volume":"56","author":"Silva","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11432-020-3144-6","article-title":"Finite-Time Command Filtered Adaptive Control for Nonlinear Systems via Immersion and Invariance","volume":"64","author":"Yu","year":"2021","journal-title":"Sci. China Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10846-018-0880-y","article-title":"Robust trajectory tracking for unmanned aircraft systems using a nonsingular terminal modified super-twisting sliding mode controller","volume":"93","author":"Espinoza","year":"2019","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.neucom.2016.08.111","article-title":"Second order sliding mode controllers for altitude control of a quadrotor UAS: Real-time implementation in outdoor environments","volume":"233","author":"Salazar","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"106513","DOI":"10.1016\/j.ymssp.2019.106513","article-title":"Neuroadaptive integral robust control of visual quadrotor for tracking a moving object","volume":"136","author":"Shao","year":"2020","journal-title":"Mech. Syst. Signal Processing"},{"key":"ref_21","first-page":"6635011","article-title":"A Dynamic Motion Tracking Control Approach for a Quadrotor Aerial Mechanical System","volume":"2020","year":"2020","journal-title":"Shock. Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1080\/21642583.2020.1851805","article-title":"Active disturbance rejection switching control of quadrotor based on robust differentiator","volume":"8","author":"Zhao","year":"2020","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.isatra.2017.01.020","article-title":"Disturbance observer based hierarchical control of coaxial-rotor UAV","volume":"67","author":"Mokhtari","year":"2017","journal-title":"ISA Trans."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s11071-017-3683-y","article-title":"Active anti-disturbance control of a quadrotor unmanned aerial vehicle using the command-filtering backstepping approach","volume":"90","author":"Aboudonia","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/TCSI.2020.3034979","article-title":"Distributed adaptive finite-time compensation control for UAV swarm with uncertain disturbances","volume":"68","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Obeid, H., Fridman, L., Laghrouche, S., and Harmouche, M. (2018, January 17\u201319). Barrier function-based adaptive integral sliding mode control. Proceedings of the 2018 IEEE Conference on Decision and Control (CDC), Miami, FL, USA.","DOI":"10.1109\/CDC.2018.8619334"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"175341","DOI":"10.1109\/ACCESS.2019.2957036","article-title":"Barrier Lyapunov function-based sliding mode control for BWB aircraft with mismatched disturbances and output constraints","volume":"7","author":"Chen","year":"2019","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"125887","DOI":"10.1109\/ACCESS.2020.3008155","article-title":"Barrier function-based adaptive neuro network sliding mode vibration control for flexible double-clamped beams with input saturation","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"106213","DOI":"10.1016\/j.ast.2020.106213","article-title":"Barrier Lyapunov function based sliding mode control for Mars atmospheric entry trajectory tracking with input saturation constraint","volume":"106","author":"Long","year":"2020","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/j.cie.2018.05.013","article-title":"Persistent UAV delivery logistics: MILP formulation and efficient heuristic","volume":"120","author":"Song","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1080\/00207721.2020.1764659","article-title":"Adaptive nonsingular terminal sliding mode control of cable-driven manipulators with time delay estimation","volume":"51","author":"Wang","year":"2020","journal-title":"Int. J. Syst. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.solener.2018.12.033","article-title":"A novel adaptive command-filtered backstepping sliding mode control for PV grid-connected system with energy storage","volume":"178","author":"Xu","year":"2019","journal-title":"Solar Energy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"106389","DOI":"10.1016\/j.ast.2020.106389","article-title":"Adaptive learning observer for spacecraft attitude control with actuator fault","volume":"108","author":"Zhu","year":"2021","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isatra.2017.11.010","article-title":"Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties","volume":"72","author":"Mofid","year":"2018","journal-title":"ISA Trans."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3428","DOI":"10.1109\/ACCESS.2020.3047659","article-title":"Adaptive terminal sliding mode control for attitude and position tracking control of quadrotor UAVs in the existence of external disturbance","volume":"9","author":"Mofid","year":"2020","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1007\/s12555-018-0489-8","article-title":"A survey of controller designs for new generation UAVs: The challenge of uncertain aerodynamic parameters","volume":"18","author":"Michailidis","year":"2020","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"031008","DOI":"10.1115\/1.4038641","article-title":"Global sliding mode control via linear matrix inequality approach for uncertain chaotic systems with input nonlinearities and multiple delays","volume":"13","author":"Afshari","year":"2018","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Mofid, O., Mobayen, S., Zhang, C., and Esakki, B. (ISA Trans., 2021). Desired tracking of delayed quadrotor UAV under model uncertainty and wind disturbance using adaptive super-twisting terminal sliding mode control, ISA Trans., in press.","DOI":"10.1016\/j.isatra.2021.06.002"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/3\/909\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:07:12Z","timestamp":1760134032000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/3\/909"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,25]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["s22030909"],"URL":"https:\/\/doi.org\/10.3390\/s22030909","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,25]]}}}