{"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/efficient-multi-agent-trajectory-planning","title":"Efficient Multi-Agent Trajectory Planning with Feasibility Guarantee using Relative Bernstein Polynomial","arxiv_id":"1909.10219","date":"2019-09-23","proceeding":null,"authors":[],"abstract":"This paper presents a new efficient algorithm which guarantees a solution for a class of multi-agent trajectory planning problems in obstacle-dense environments. Our algorithm combines the advantages of both grid-based and optimization-based approaches, and generates safe, dynamically feasible trajectories without suffering from an erroneous optimization setup such as imposing infeasible collision constraints. We adopt a sequential optimization method with \\textit{dummy agents} to improve the scalability of the algorithm, and utilize the convex hull property of Bernstein and relative Bernstein polynomial to replace non-convex collision avoidance constraints to convex ones. The proposed method can compute the trajectory for 64 agents on average 6.36 seconds with Intel Core i7-7700 @ 3.60GHz CPU and 16G RAM, and it reduces more than $50\\%$ of the objective cost compared to our previous work. We validate the proposed algorithm through simulation and flight tests.","url_abs":"https://arxiv.org/abs/1909.10219v2","url_pdf":"https://arxiv.org/pdf/1909.10219v2.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":"efficient-multi-agent-trajectory-planning","repo_url":"https://github.com/qwerty35/swarm_simulator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"CPU"},{"task_slug":"collision-avoidance","task_name":"Collision Avoidance"},{"task_slug":"trajectory-planning","task_name":"Trajectory Planning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}