Proposed Approximate Dynamic Programming for Pathfinding under Visible Uncertainty

TL;DR

This paper introduces a new approach to pathfinding under uncertainty, modeling the problem with measure-theoretic probability and proposing an approximate dynamic programming solution to find safe paths with visibility considerations.

Contribution

It defines the safest-with-sight pathfinding problem and develops a recursive probability model, proposing an approximate dynamic programming method for its solution.

Findings

Recursive probability definition for path selection

Approximate solution based on measure-theoretic probability

Framework for pathfinding with visibility and uncertainty

Abstract

Continuing our preleminary work \cite{knowles14}, we define the safest-with-sight pathfinding problems and explore its solution using techniques borrowed from measure-theoretic probability theory. We find a simple recursive definition for the probability that an ideal pathfinder will select an edge in a given scenario of an uncertain network where edges have probabilities of failure and vertices provide "vision" of edges via lines-of-sight. We propose an approximate solution based on our theoretical findings that would borrow techniques from approximate dynamic programming.