Minimizing Task Space Frechet Error via Efficient Incremental Graph Search

TL;DR

This paper introduces an efficient anytime algorithm that plans collision-free paths in configuration space, closely following a desired task space path using discrete Frechet distance, with proven asymptotic optimality.

Contribution

It presents a novel incremental graph search method leveraging computational geometry to improve path planning accuracy and efficiency in manipulation tasks.

Findings

Outperforms state-of-the-art planners in manipulation problems

Demonstrates effective densification strategies

Provides a proof sketch of asymptotic optimality

Abstract

We present an anytime algorithm that generates a collision-free configuration-space path that closely follows a desired path in task space, according to the discrete Frechet distance. By leveraging tools from computational geometry, we approximate the search space using a cross-product graph. We use a variant of Dijkstra's graph-search algorithm to efficiently search for and iteratively improve the solution. We compare multiple proposed densification strategies and empirically show that our algorithm outperforms a set of state-of-the-art planners on a range of manipulation problems. Finally, we offer a proof sketch of the asymptotic optimality of our algorithm.