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arXiv · 1409.3360

Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications

Krishnendu Chatterjee·Martin Chmelík·Raghav Gupta·Ayush Kanodia
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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.

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Krishnendu Chatterjee, Martin Chmelík, Raghav Gupta, Ayush Kanodia. 2015-02-18. Qualitative Analysis of POMDPs with Temporal Logic Specifications for Robotics Applications. https://arxiv.org/abs/1409.3360

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