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This study proposes Timed-Elastic-Band-Based Variable Splitting (TEB-VS), a novel framework that integrates variable splitting (VS)\u2014a constrained optimization technique\u2014with the classical Timed-Elastic-Band (TEB) algorithm. Unlike incremental modifications to TEB, TEB-VS introduces a systematic combination of VS and TEB to decompose non-convex global constraints into tractable subproblems while leveraging symmetry principles for balanced multi-objective control (e.g., velocity, acceleration, and obstacle avoidance). Experimental results demonstrate that TEB-VS achieves a 46.5% improvement in motion stability over traditional TEB in obstacle-free simulations and a 37% enhancement in dynamic obstacle scenarios. Real-world tests show a 26.7% reduction in angular velocity oscillations, with computational efficiency comparable to TEB. The framework\u2019s effectiveness in harmonizing trajectory smoothness and dynamic adaptability is validated through extensive simulations and TurtleBot2 experiments.<\/jats:p>","DOI":"10.3390\/sym17060848","type":"journal-article","created":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T06:25:04Z","timestamp":1748499904000},"page":"848","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Timed-Elastic-Band-Based Variable Splitting for Autonomous Trajectory Planning"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-0791-7108","authenticated-orcid":false,"given":"Hao","family":"Zhu","sequence":"first","affiliation":[{"name":"State Key Laboratory of ASIC and Systems, The Institute of Brain-Inspired Circuits and Systems, Fudan University, Shanghai 200437, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kefan","family":"Jin","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Marine Intelligent Equipment and System, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Gao","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Marine Intelligent Equipment and System, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jialin","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and Systems, The Institute of Brain-Inspired Circuits and Systems, Fudan University, Shanghai 200437, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard","family":"Shi","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Washington, Seattle, WA 98195, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3424","DOI":"10.1109\/TVT.2020.2968343","article-title":"Energy-efficient UAV-assisted mobile edge computing: Resource allocation and trajectory optimization","volume":"69","author":"Li","year":"2020","journal-title":"IEEE Trans. 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