{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T16:47:23Z","timestamp":1778690843514,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T00:00:00Z","timestamp":1617321600000},"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>Multirotor Unmanned Aerial Vehicles (UAVs) play an imperative role in many real-world applications in a variety of scenarios characterized by a high density of obstacles with different heights. Due to the complicated operation areas of UAVs and complex constraints associated with the assigned mission, there should be a suitable path to fly. Therefore, the most relevant challenge is how to plan a flyable path for a UAV without collisions with obstacles. This paper demonstrates how a flyable and continuous trajectory was constructed by using any-angle pathfinding algorithms, which are Basic Theta*, Lazy Theta*, and Phi* algorithms for a multirotor UAV in a cluttered environment. The three algorithms were modified by adopting a modified cost function during their implementation that considers the elevation of nodes. First, suitable paths are generated by using a modified version of the three algorithms. After that, four B\u00e9zier curves-based approaches are proposed to smooth the generated paths to be converted to flyable paths (trajectories). To determine the most suitable approach, particularly when searching for an optimal and collision-free trajectory design, an innovative evaluation process is proposed and applied in a variety of different size environments. The evaluation process results show high success rates of the four approaches; however, the approach with the highest success rate is adopted. Finally, based on the results of the evaluation process, a novel algorithm is proposed to increase the efficiency of the selected approach to the optimality in the construction process of the trajectory.<\/jats:p>","DOI":"10.3390\/s21072460","type":"journal-article","created":{"date-parts":[[2021,4,2]],"date-time":"2021-04-02T04:13:51Z","timestamp":1617336831000},"page":"2460","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["B\u00e9zier Curves-Based Optimal Trajectory Design for Multirotor UAVs with Any-Angle Pathfinding Algorithms"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2942-8249","authenticated-orcid":false,"given":"Haitham AL","family":"Satai","sequence":"first","affiliation":[{"name":"School of Electronics Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5879-6991","authenticated-orcid":false,"given":"Musaddak M. Abdul","family":"Zahra","sequence":"additional","affiliation":[{"name":"Computer Techniques Engineering Department, Al-Mustaqbal University College, Babylon 51001, Iraq"},{"name":"Electrical Engineering Department, College of Engineering, University of Babylon, Babylon 51001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6900-3443","authenticated-orcid":false,"given":"Zaid I.","family":"Rasool","sequence":"additional","affiliation":[{"name":"Computer Techniques Engineering Department, Al-Mustaqbal University College, Babylon 51001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ridhab Sami","family":"Abd-Ali","sequence":"additional","affiliation":[{"name":"Computer Techniques Engineering Department, Al-Mustaqbal University College, Babylon 51001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4926-2189","authenticated-orcid":false,"given":"Catalin I.","family":"Pruncu","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Imperial Colle London, Exhibition Rd., London SW7 2AZ, UK"},{"name":"Design, Manufacturing &amp; Engineering Management, University of Strathclyde, Glasgow G1 1XJ, Scotland, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,2]]},"reference":[{"key":"ref_1","first-page":"1646","article-title":"Review of unmanned aircraft system (UAS)","volume":"2","author":"Gupta","year":"2013","journal-title":"Int. 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