{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T05:08:05Z","timestamp":1770959285493,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T00:00:00Z","timestamp":1626220800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSERC Alliance-AI Advance Program","award":["202102595"],"award-info":[{"award-number":["202102595"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>This paper presents a trajectory generation method for a nonlinear system under closed-loop control (here a quadrotor drone) motivated by the Nonlinear Model Predictive Control (NMPC) method. Unlike NMPC, the proposed method employs a closed-loop system dynamics model within the optimization problem to efficiently generate reference trajectories in real time. We call this approach the Nonlinear Model Predictive Horizon (NMPH). The closed-loop model used within NMPH employs a feedback linearization control law design to decrease the nonconvexity of the optimization problem and thus achieve faster convergence. For robust trajectory planning in a dynamically changing environment, static and dynamic obstacle constraints are supported within the NMPH algorithm. Our algorithm is applied to a quadrotor system to generate optimal reference trajectories in 3D, and several simulation scenarios are provided to validate the features and evaluate the performance of the proposed methodology.<\/jats:p>","DOI":"10.3390\/robotics10030090","type":"journal-article","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T21:56:51Z","timestamp":1626299811000},"page":"90","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Nonlinear Model Predictive Horizon for Optimal Trajectory Generation"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8295-8356","authenticated-orcid":false,"given":"Younes","family":"Al Younes","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada"}]},{"given":"Martin","family":"Barczyk","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/0005-1098(78)90001-8","article-title":"Model predictive heuristic control: Applications to industrial processes","volume":"14","author":"Richalet","year":"1978","journal-title":"Automatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/0005-1098(89)90002-2","article-title":"Model predictive control: Theory and practice\u2014A survey","volume":"25","author":"Garcia","year":"1989","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gr\u00fcne, L., and Pannek, J. 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