Hierarchical planning with state abstractions for temporal task specifications

Abstract

We often specify tasks for a robot using temporal language that can include different levels of abstraction. For example, the 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 syntactically co-safe Linear Temporal Logic (sc-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 path planning tasks, and this number only increases as the size of the environment domain increases. In a cleanup world domain, AP-MDP performs faster in over $98\%$ of tasks. 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 two drones, demonstrating that our approach enables robots to efficiently solve temporal commands at different levels of abstraction in both indoor and outdoor environments.

Keywords: Hierarchical task planning; Language; Linear temporal logic.