{"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/planning-with-linear-temporal-logic","title":"Planning with Linear Temporal Logic Specifications: Handling Quantifiable and Unquantifiable Uncertainty","arxiv_id":"2502.19603","date":"2025-02-26","proceeding":null,"authors":["Pian Yu","Yong Li","David Parker","Marta Kwiatkowska"],"abstract":"This work studies the planning problem for robotic systems under both quantifiable and unquantifiable uncertainty. The objective is to enable the robotic systems to optimally fulfill high-level tasks specified by Linear Temporal Logic (LTL) formulas. To capture both types of uncertainty in a unified modelling framework, we utilise Markov Decision Processes with Set-valued Transitions (MDPSTs). We introduce a novel solution technique for the optimal robust strategy synthesis of MDPSTs with LTL specifications. To improve efficiency, our work leverages limit-deterministic B\\\"uchi automata (LDBAs) as the automaton representation for LTL to take advantage of their efficient constructions. To tackle the inherent nondeterminism in MDPSTs, which presents a significant challenge for reducing the LTL planning problem to a reachability problem, we introduce the concept of a Winning Region (WR) for MDPSTs. Additionally, we propose an algorithm for computing the WR over the product of the MDPST and the LDBA. Finally, a robust value iteration algorithm is invoked to solve the reachability problem. We validate the effectiveness of our approach through a case study involving a mobile robot operating in the hexagonal world, demonstrating promising efficiency gains.","url_abs":"https://arxiv.org/abs/2502.19603v1","url_pdf":"https://arxiv.org/pdf/2502.19603v1.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":"planning-with-linear-temporal-logic","repo_url":"https://github.com/piany/MDPST-full-LTL","is_official":1,"mentioned_in_paper":0,"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}