On Probabilistic Completeness of Probabilistic Cell Decomposition

TL;DR

This paper provides the first detailed proof that Probabilistic Cell Decomposition (PCD), a path planning method combining cell decomposition and sampling, is probabilistically complete, ensuring it can find a path if one exists with high probability.

Contribution

The paper offers the first rigorous proof of probabilistic completeness for PCD, validating its effectiveness in path planning.

Findings

PCD is proven to be probabilistically complete.

Lazy evaluation and supervised sampling enhance PCD performance.

The proof confirms PCD's reliability in path planning scenarios.

Abstract

Probabilistic Cell Decomposition (PCD) is a probabilistic path planning method combining the concepts of approximate cell decomposition with probabilistic sampling. It has been shown that the use of lazy evaluation techniques and supervised sampling in important areas result in a high performance path planning method. Even if it was postulated before that PCD is probabilistically complete, we present a detailed proof of probabilistic completeness here for the first time.