Time-Optimal Navigation in Uncertain Environments with High-Level Specifications

TL;DR

This paper develops a method for time-efficient control policy synthesis in mixed observable Markov decision processes that ensures high-level specifications are met, demonstrated on navigation tasks with partial observability.

Contribution

It introduces an exact dynamic programming approach and a point-based approximation for control synthesis in MOMDPs with temporal logic constraints.

Findings

The exact dynamic programming method computes optimal policies.

The approximation provides a lower bound on satisfaction probability.

The approach outperforms standard strategies in navigation tasks.

Abstract

Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that minimizes the expected time to complete the control task while satisfying syntactically co-safe Linear Temporal Logic (scLTL) specifications. First, we present an exact dynamic programming update to compute the value function. Afterwards, we propose a point-based approximation, which allows us to compute a lower bound of the closed-loop probability of satisfying the specifications. The effectiveness of the proposed approach and comparisons with standard strategies are shown on high-fidelity navigation tasks with partially observable static obstacles.