{"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/real-time-spatial-trajectory-planning-for","title":"Real-Time Spatial Trajectory Planning for Urban Environments Using Dynamic Optimization","arxiv_id":"2305.02621","date":"2023-05-04","proceeding":null,"authors":["Jona Ruof","Max Bastian Mertens","Michael Buchholz","Klaus Dietmayer"],"abstract":"Planning trajectories for automated vehicles in urban environments requires methods with high generality, long planning horizons, and fast update rates. Using a path-velocity decomposition, we contribute a novel planning framework, which generates foresighted trajectories and can handle a wide variety of state and control constraints effectively. In contrast to related work, the proposed optimal control problems are formulated over space rather than time. This spatial formulation decouples environmental constraints from the optimization variables, which allows the application of simple, yet efficient shooting methods. To this end, we present a tailored solution strategy based on ILQR, in the Augmented Lagrangian framework, to rapidly minimize the trajectory objective costs, even under infeasible initial solutions. Evaluations in simulation and on a full-sized automated vehicle in real-world urban traffic show the real-time capability and versatility of the proposed approach.","url_abs":"https://arxiv.org/abs/2305.02621v2","url_pdf":"https://arxiv.org/pdf/2305.02621v2.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"real-time-spatial-trajectory-planning-for","repo_url":"https://github.com/joruof/tpl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}