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 (\sim15 \mus/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.
