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This problem is challenging because the inverse kinematics of manipulators are highly nonlinear and complexly coupled. To address this challenge, the bald eagle search optimization algorithm is introduced. This algorithm combines the advantages of evolutionary and swarm techniques, making it more effective at solving nonlinear problems and improving search efficiency. Due to the tendency of the algorithm to fall into local optima, the L\u00e9vy flight strategy is introduced to enhance its performance. This strategy adopts a heavy-tailed distribution to generate long-distance jumps, thereby preventing the algorithm from becoming trapped in local optima and enhancing its global search efficiency. The experiments first evaluated the accuracy and robustness of the proposed algorithm based on the inverse kinematics problem of manipulators, achieving a solution accuracy of up to 10\u221218 m. Subsequently, the proposed algorithm was compared with other algorithms using the CEC2017 test functions. The results showed that the improved algorithm significantly outperformed the original in accuracy, convergence speed, and stability. Specifically, it achieved over 70% improvement in both standard deviation and mean for several test functions, demonstrating the effectiveness of the L\u00e9vy flight strategy in enhancing global search capabilities. Furthermore, the practicality of the proposed algorithm was verified through two real engineering optimization problems.<\/jats:p>","DOI":"10.3390\/biomimetics9100627","type":"journal-article","created":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T07:58:32Z","timestamp":1729065512000},"page":"627","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Improved Bald Eagle Search Optimization Algorithm for the Inverse Kinematics of Robotic Manipulators"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4336-1431","authenticated-orcid":false,"given":"Guojun","family":"Zhao","sequence":"first","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5886-1992","authenticated-orcid":false,"given":"Bo","family":"Tao","sequence":"additional","affiliation":[{"name":"Precision Manufacturing Research Institute, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Du","family":"Jiang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juntong","family":"Yun","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hanwen","family":"Fan","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"eaan5074","DOI":"10.1126\/scirobotics.aan5074","article-title":"Review on space robotics: Toward top-level science through space exploration","volume":"2","author":"Gao","year":"2017","journal-title":"Sci. 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