Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications

TL;DR

This paper presents a practical heuristic approach to analyze POMDPs with temporal logic specifications, enabling robotics applications to verify almost-sure satisfaction of complex objectives despite theoretical intractability.

Contribution

The paper introduces heuristics and an implementation for qualitative analysis of POMDPs with parity objectives, addressing the intractability in robotics contexts.

Findings

Practical heuristics improve analysis efficiency.

First implementation for qualitative POMDP analysis in robotics.

Successfully applied to well-known robotics POMDP examples.

Abstract

We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.