A Fast Randomized Method to Find Homotopy Classes for Socially-Aware Navigation

TL;DR

This paper presents a fast randomized algorithm for identifying diverse homotopy classes of paths in social navigation, outperforming traditional methods in speed and diversity while maintaining path quality.

Contribution

The paper introduces a novel randomized approach for efficiently finding diverse homotopy classes in social navigation scenarios, based on Voronoi graph search.

Findings

Faster than Yen's algorithm in finding homotopy classes

Produces more diverse paths with minimal quality loss

Empirically validated on social navigation tasks

Abstract

We introduce and show preliminary results of a fast randomized method that finds a set of K paths lying in distinct homotopy classes. We frame the path planning task as a graph search problem, where the navigation graph is based on a Voronoi diagram. The search is biased by a cost function derived from the social force model that is used to generate and select the paths. We compare our method to Yen's algorithm, and empirically show that our approach is faster to find a subset of homotopy classes. Furthermore our approach computes a set of more diverse paths with respect to the baseline while obtaining a negligible loss in path quality.