{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/theta-any-angle-path-planning-on-grids","title":"Theta*: Any-Angle Path Planning on Grids","arxiv_id":"1401.3843","date":"2014-01-16","proceeding":null,"authors":["Kenny Daniel","Alex Nash","Sven Koenig","Ariel Felner"],"abstract":"Grids with blocked and unblocked cells are often used to represent terrain in\nrobotics and video games. However, paths formed by grid edges can be longer\nthan true shortest paths in the terrain since their headings are artificially\nconstrained. We present two new correct and complete any-angle path-planning\nalgorithms that avoid this shortcoming. Basic Theta* and Angle-Propagation\nTheta* are both variants of A* that propagate information along grid edges\nwithout constraining paths to grid edges. Basic Theta* is simple to understand\nand implement, fast and finds short paths. However, it is not guaranteed to\nfind true shortest paths. Angle-Propagation Theta* achieves a better worst-case\ncomplexity per vertex expansion than Basic Theta* by propagating angle ranges\nwhen it expands vertices, but is more complex, not as fast and finds slightly\nlonger paths. We refer to Basic Theta* and Angle-Propagation Theta*\ncollectively as Theta*. Theta* has unique properties, which we analyze in\ndetail. We show experimentally that it finds shorter paths than both A* with\npost-smoothed paths and Field D* (the only other version of A* we know of that\npropagates information along grid edges without constraining paths to grid\nedges) with a runtime comparable to that of A* on grids. Finally, we extend\nTheta* to grids that contain unblocked cells with non-uniform traversal costs\nand introduce variants of Theta* which provide different tradeoffs between path\nlength and runtime.","url_abs":"http://arxiv.org/abs/1401.3843v1","url_pdf":"http://arxiv.org/pdf/1401.3843v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"theta-any-angle-path-planning-on-grids","repo_url":"https://github.com/PathPlanning/ORCA-algorithm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1401.3843","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}