{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T17:00:31Z","timestamp":1780074031719,"version":"3.54.0"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T00:00:00Z","timestamp":1756771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Sichuan Province of China","award":["2024NSFSC0181"],"award-info":[{"award-number":["2024NSFSC0181"]}]},{"name":"Natural Science Foundation of Sichuan Province of China","award":["24R1437300"],"award-info":[{"award-number":["24R1437300"]}]},{"name":"Natural Science Foundation of Sichuan Province of China","award":["201901080001"],"award-info":[{"award-number":["201901080001"]}]},{"name":"Natural Science Foundation of Shanghai Municipality of China","award":["2024NSFSC0181"],"award-info":[{"award-number":["2024NSFSC0181"]}]},{"name":"Natural Science Foundation of Shanghai Municipality of China","award":["24R1437300"],"award-info":[{"award-number":["24R1437300"]}]},{"name":"Natural Science Foundation of Shanghai Municipality of China","award":["201901080001"],"award-info":[{"award-number":["201901080001"]}]},{"DOI":"10.13039\/501100012130","name":"Aeronautical Science Foundation of China","doi-asserted-by":"publisher","award":["2024NSFSC0181"],"award-info":[{"award-number":["2024NSFSC0181"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012130","name":"Aeronautical Science Foundation of China","doi-asserted-by":"publisher","award":["24R1437300"],"award-info":[{"award-number":["24R1437300"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012130","name":"Aeronautical Science Foundation of China","doi-asserted-by":"publisher","award":["201901080001"],"award-info":[{"award-number":["201901080001"]}],"id":[{"id":"10.13039\/501100012130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a hierarchical optimization framework combining Bayesian and pseudospectral approaches is developed to solve the challenging problem of hybrid trajectory planning for energy-augmented hypersonic skip\u2013glide vehicles that have plane symmetry. Traditional trajectory optimization methods usually deal with discrete energy injection timing and continuous flight control variables separately, yielding suboptimal solutions. To achieve global optimality, this proposed framework optimizes the discrete and continuous variables simultaneously, conducting Bayesian optimization for discrete global search and hp-adaptive pseudospectral algorithm for local continuous optimization. A rigorous dynamic model, considering Earth\u2019s oblateness, rotation, aerodynamic interactions, and thrust dynamics, is established to ensure high-fidelity trajectory simulation. Numerical simulation through three representative tests indicates significant improvements: The hp-adaptive pseudospectral method achieves over 20% higher computational efficiency and accuracy compared to standard pseudospectral methods. Bayesian optimization demonstrates rapid global convergence within 22 iterations, achieving the optimal single augmentation timing that enhances flight range by up to 55.08%. Further, comprehensive joint optimization with double energy augmentation yields an additional 7.5% range extension compared to randomly selected augmentation timings. The results verify that the proposed hierarchical framework substantially improves the planned trajectory performance and adaptability to the skip\u2013glide trajectories with hybrid maneuver.<\/jats:p>","DOI":"10.3390\/sym17091430","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T08:23:38Z","timestamp":1756801418000},"page":"1430","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hybrid Trajectory Planning for Energy-Augmented Skip\u2013Glide Vehicles via Hierarchical Bayesian Optimization"],"prefix":"10.3390","volume":"17","author":[{"given":"Lianxing","family":"Wang","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3184-3679","authenticated-orcid":false,"given":"Yuankai","family":"Li","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"Systems and Artificial Intelligence Key Laboratory of Sichuan Province, University of Electronic Science and Technology of China, Chengdu 611731, China"},{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guowei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4345-1613","authenticated-orcid":false,"given":"Xiaoliang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,2]]},"reference":[{"key":"ref_1","first-page":"23","article-title":"Analysis of energy supply strategy for hypersonic skip-glide trajectory","volume":"41","author":"Chai","year":"2020","journal-title":"Tactical Missile Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s42401-020-00069-4","article-title":"Adaptive Radau pseudo-spectral optimization for descending trajectory of a hypersonic cruise vehicle","volume":"3","author":"Feng","year":"2020","journal-title":"Aerosp. 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