{"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/safe-optimal-real-time-trajectory-planning","title":"Safe, Optimal, Real-time Trajectory Planning with a Parallel Constrained Bernstein Algorithm","arxiv_id":"2003.01758","date":"2020-03-03","proceeding":null,"authors":["Shreyas Kousik","Bohao Zhang","Pengcheng Zhao","Ram Vasudevan"],"abstract":"To move through the world, mobile robots typically use a receding-horizon strategy, wherein they execute an old plan while computing a new plan to incorporate new sensor information. A plan should be dynamically feasible, meaning it obeys constraints like the robot's dynamics and obstacle avoidance; it should have liveness, meaning the robot does not stop to plan so frequently that it cannot accomplish tasks; and it should be optimal, meaning that the robot tries to satisfy a user-specified cost function such as reaching a goal location as quickly as possible. Reachability-based Trajectory Design (RTD) is a planning method that can generate provably dynamically-feasible plans. However, RTD solves a nonlinear polynmial optimization program at each planning iteration, preventing optimality guarantees; furthermore, RTD can struggle with liveness because the robot must brake to a stop when the solver finds local minima or cannot find a feasible solution. This paper proposes RTD*, which certifiably finds the globally optimal plan (if such a plan exists) at each planning iteration. This method is enabled by a novel Parallelized Constrained Bernstein Algorithm (PCBA), which is a branch-and-bound method for polynomial optimization. The contributions of this paper are: the implementation of PCBA; proofs of bounds on the time and memory usage of PCBA; a comparison of PCBA to state of the art solvers; and the demonstration of PCBA/RTD* on a mobile robot. RTD* outperforms RTD in terms of optimality and liveness for real-time planning in a variety of environments with randomly-placed obstacles.","url_abs":"https://arxiv.org/abs/2003.01758v1","url_pdf":"https://arxiv.org/pdf/2003.01758v1.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":"safe-optimal-real-time-trajectory-planning","repo_url":"https://github.com/ramvasudevan/GlobOptBernstein","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}