{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:01:29Z","timestamp":1762351289683,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangdong Major Science and Technology Project","award":["2019B090919003"],"award-info":[{"award-number":["2019B090919003"]}]},{"DOI":"10.13039\/501100012245","name":"Science and Technology Planning Project of Guangdong Province","doi-asserted-by":"publisher","award":["2017B090913001"],"award-info":[{"award-number":["2017B090913001"]}],"id":[{"id":"10.13039\/501100012245","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["2020A1515011393"],"award-info":[{"award-number":["2020A1515011393"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the rapid development of robotics, wheeled mobile robots are widely used in smart factories to perform navigation tasks. In this paper, an optimal trajectory planning method based on an improved dolphin swarm algorithm is proposed to balance localization uncertainty and energy efficiency, such that a minimum total cost trajectory is obtained for wheeled mobile robots. Since environmental information has different effects on the robot localization process at different positions, a novel localizability measure method based on the likelihood function is presented to explicitly quantify the localization ability of the robot over a prior map. To generate the robot trajectory, we incorporate localizability and energy efficiency criteria into the parameterized trajectory as the cost function. In terms of trajectory optimization issues, an improved dolphin swarm algorithm is then proposed to generate better localization performance and more energy efficiency trajectories. It utilizes the proposed adaptive step strategy and learning strategy to minimize the cost function during the robot motions. Simulations are carried out in various autonomous navigation scenarios to validate the efficiency of the proposed trajectory planning method. Experiments are performed on the prototype \u201cForbot\u201d four-wheel independently driven-steered mobile robot; the results demonstrate that the proposed method effectively improves energy efficiency while reducing localization errors along the generated trajectory.<\/jats:p>","DOI":"10.3390\/s21020335","type":"journal-article","created":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T20:45:42Z","timestamp":1609965942000},"page":"335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Optimal Trajectory Planning for Wheeled Mobile Robots under Localization Uncertainty and Energy Efficiency Constraints"],"prefix":"10.3390","volume":"21","author":[{"given":"Xiaolong","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youmin","family":"Rong","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gen","family":"Li","sequence":"additional","affiliation":[{"name":"Guangzhou Institute of Advanced Technology, Chinese Academy of Sciences, Guangzhou 511400, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1435-2774","authenticated-orcid":false,"given":"Chao","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hern\u00e1ndez-Guzm\u00e1n, V.M., Silva-Ortigoza, R., Tavera-Mosqueda, S., Marcelino-Aranda, M., and Marciano-Melchor, M. 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