Planning with Linear Temporal Logic Specifications: Handling Quantifiable and Unquantifiable Uncertainty

2025-02-26

AI Summary

This work addresses optimal robust planning for robotic high-level tasks specified in Linear Temporal Logic (LTL) under both quantifiable and unquantifiable uncertainties. To jointly model these uncertainty types, we propose Set-Valued Transition Markov Decision Processes (MDPSTs). We introduce, for the first time, the notion of Winning Regions (WRs) to reformulate LTL planning as a robust reachability problem and develop an efficient WR computation algorithm. Integrating Limit-Deterministic Büchi Automata (LDBAs), MDPST modeling, WR analysis, and robust value iteration, we establish an end-to-end planning framework. Evaluated on a hexagonal-grid mobile robot navigation task, our approach achieves significant improvements in planning efficiency over baseline methods while demonstrating strong robustness against model mismatch and environmental disturbances.

Technology Category

• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Intelligent Robots: State Estimation
• Multiagent Systems: Multiagent Planning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Robotic planning under quantifiable and unquantifiable uncertainty
• Optimal fulfillment of LTL-specified high-level tasks
• Robust strategy synthesis using MDPSTs and LDBAs

Innovation

• MDPSTs for uncertainty modeling
• LDBAs enhance LTL efficiency
• Winning Region concept introduced