# Planning with State Abstractions for Non-Markovian Task Specifications

## TL;DR

This paper introduces the AP-MDP framework that combines hierarchical abstractions and temporal logic to enable robots to interpret and efficiently execute complex, non-Markovian language commands involving both spatial and temporal aspects.

## Contribution

The paper presents the novel AP-MDP approach that integrates LTL automata with hierarchical MDPs for handling non-Markovian, multi-level language commands in robotic planning.

## Key findings

- AP-MDP outperforms non-hierarchical methods in over 95% of tasks.
- The approach scales better with environment size.
- A new dataset of language commands was created and tested.

## Abstract

Often times, we specify tasks for a robot using temporal language that can also span different levels of abstraction. The example command ``go to the kitchen before going to the second floor'' contains spatial abstraction, given that ``floor'' consists of individual rooms that can also be referred to in isolation ("kitchen", for example). There is also a temporal ordering of events, defined by the word "before". Previous works have used Linear Temporal Logic (LTL) to interpret temporal language (such as "before"), and Abstract Markov Decision Processes (AMDPs) to interpret hierarchical abstractions (such as "kitchen" and "second floor"), separately. To handle both types of commands at once, we introduce the Abstract Product Markov Decision Process (AP-MDP), a novel approach capable of representing non-Markovian reward functions at different levels of abstractions. The AP-MDP framework translates LTL into its corresponding automata, creates a product Markov Decision Process (MDP) of the LTL specification and the environment MDP, and decomposes the problem into subproblems to enable efficient planning with abstractions. AP-MDP performs faster than a non-hierarchical method of solving LTL problems in over 95% of tasks, and this number only increases as the size of the environment domain increases. We also present a neural sequence-to-sequence model trained to translate language commands into LTL expression, and a new corpus of non-Markovian language commands spanning different levels of abstraction. We test our framework with the collected language commands on a drone, demonstrating that our approach enables a robot to efficiently solve temporal commands at different levels of abstraction.