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This formulation captures both spatial feasibility and temporal logic within a unified matrix representation, enabling efficient synthesis of feasible trajectories via graph-based search algorithms. The method supports task updates and traffic-aware replanning by dynamically updating the underlying matrix structures. We demonstrate the approach using representative parking scenarios with realistic constraints, including one-way lanes, static and dynamic obstacles, and mid-mission task changes. The proposed matrix fusion strategy offers a scalable and rigorous framework for mission-critical autonomous navigation.<\/jats:p>","DOI":"10.3390\/robotics14110171","type":"journal-article","created":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T08:59:46Z","timestamp":1763715586000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Matrix-Guided Safe Motion Planning for Smart Parking Systems"],"prefix":"10.3390","volume":"14","author":[{"given":"Dewan Mohammed Abdul","family":"Ahad","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, Charlotte, NC 28223, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dipankar","family":"Maity","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of North Carolina at Charlotte, Charlotte, NC 28223, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Miao, X., and Duan, M. 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