{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:47:40Z","timestamp":1764859660910,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T00:00:00Z","timestamp":1718755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\/MCTES (PIDDAC)","award":["10.54499\/PTDC\/EEI- AUT\/3522\/2020"],"award-info":[{"award-number":["10.54499\/PTDC\/EEI- AUT\/3522\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This article presents an innovative approach to the design of a safe adaptive backstepping control system. Tailored specifically for underactuated marine robots, the system utilizes simple sensors for enhanced practicality and efficiency. Given their operation in diverse oceanic environments fraught with various sources of uncertainties, ensuring the system\u2019s safe and robust behavior holds paramount importance in the control literature. To address this concern, this paper introduces a control strategy designed to ensure robustness at both the kinematic and dynamic levels. By emphasizing the compensation for the system uncertainties, the design integrates a straightforward fuzzy system structure. To further ensure the system\u2019s safety, a funnel surface is defined, followed by the design of a suitable nonlinear sliding surface as a function of the funnel and tracking error. Using Lyapunov theory, the study formally establishes the Semi-globally Practically Finite-time Stability of the closed-loop system, validated through simulations conducted on underactuated marine robots.<\/jats:p>","DOI":"10.3390\/s24123974","type":"journal-article","created":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T08:06:06Z","timestamp":1718784366000},"page":"3974","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Safe Robust Adaptive Motion Control for Underactuated Marine Robots"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7297-5769","authenticated-orcid":false,"given":"G. Reza","family":"Nazmara","sequence":"first","affiliation":[{"name":"SYSTEC, ARISE, and Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7105-0505","authenticated-orcid":false,"given":"A. Pedro","family":"Aguiar","sequence":"additional","affiliation":[{"name":"SYSTEC, ARISE, and Department of Electrical and Computer Engineering, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"116204","DOI":"10.1016\/j.oceaneng.2023.116204","article-title":"Improved adaptive twisting sliding mode control for trajectory tracking of an AUV subject to uncertainties","volume":"297","author":"Li","year":"2024","journal-title":"J. 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Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"102321","DOI":"10.1109\/ACCESS.2019.2927810","article-title":"Finite-Time Trajectory Tracking Control for Uncertain Underactuated Marine Surface Vessels","volume":"7","author":"Zhang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2671","DOI":"10.1080\/00207179.2022.2111365","article-title":"Adaptive finite-time impedance backstepping control for uncertain robotic systems interacting with unknown environments","volume":"96","author":"Ahmadi","year":"2023","journal-title":"Int. J. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/S0005-1098(01)00199-6","article-title":"Global tracking control of underactuated ships by Lyapunov\u2019s direct method","volume":"38","author":"Jiang","year":"2002","journal-title":"J. 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