Conformal Temporal Logic Planning using Large Language Models

This paper addresses planning problems for mobile robots. We consider missions that require accomplishing multiple high-level sub-tasks, expressed in natural language (NL), in a temporal and logical order. To formally define the mission, we treat these sub-tasks as atomic predicates in a Linear Temporal Logic (LTL) formula. We refer to this task specification framework as LTL-NL. Our goal is to design plans, defined as sequences of robot actions, accomplishing LTL-NL tasks. This action planning problem cannot be solved directly by existing LTL planners because of the NL nature of atomic predicates. To address it, we propose HERACLEs, a hierarchical neuro-symbolic planner that relies on a novel integration of (i) existing symbolic planners generating high-level task plans determining the order at which the NL sub-tasks should be accomplished; (ii) pre-trained Large Language Models (LLMs) to design sequences of robot actions based on these task plans; and (iii) conformal prediction acting as a formal interface between (i) and (ii) and managing uncertainties due to LLM imperfections. We show, both theoretically and empirically, that HERACLEs can achieve user-defined mission success rates. Finally, we provide comparative experiments demonstrating that HERACLEs outperforms LLM-based planners that require the mission to be defined solely using NL. Additionally, we present examples demonstrating that our approach enhances user-friendliness compared to conventional symbolic approaches.