RichMap: A Reachability Map Balancing Precision, Efficiency, and Flexibility for Rich Robot Manipulation Tasks

TL;DR

RichMap is a high-precision reachability map that balances accuracy, efficiency, and flexibility for robot manipulation, validated by extensive experiments and applications.

Contribution

Introduces RichMap, a novel reachability map with theoretical guarantees, efficient construction, and versatile applications in robot manipulation tasks.

Findings

Achieves >98% prediction accuracy and 1-2% false positive rate.

Enables fast large-batch queries (~15 μs/query).

Improves cross-embodiment diffusion policy transfer by up to 26%.

Abstract

This paper presents RichMap, a high-precision reachability map representation designed to balance efficiency and flexibility for versatile robot manipulation tasks. By refining the classic grid-based structure, we propose a streamlined approach that achieves performance close to compact map forms (e.g., RM4D) while maintaining structural flexibility. Our method utilizes theoretical capacity bounds on $\mathbb{S}^2$ (or $SO(3)$) to ensure rigorous coverage and employs an asynchronous pipeline for efficient construction. We validate the map against comprehensive metrics, pursuing high prediction accuracy ($>98\%$), low false positive rates ($1\sim2\%$), and fast large-batch query ($\sim$15 $\mu$s/query). We extend the framework applications to quantify robot workspace similarity via maximum mean discrepancy (MMD) metrics and demonstrate energy-based guidance for diffusion policy transfer, achieving up to $26\%$ improvement for cross-embodiment scenarios in the block pushing experiment.