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This paper introduces RichMap, a reachability map representation that balances precision, efficiency, and flexibility by refining grid-based structures using theoretical capacity bounds on $\mathbb{S}^2$ or $SO(3)$ for rigorous coverage. An asynchronous pipeline enables efficient map construction, achieving high prediction accuracy ($>98\%$) and low false positive rates ($1\sim2\%$) with fast query times ($\sim$15 $渭$s/query). RichMap's utility is demonstrated through workspace similarity quantification using MMD and energy-based guidance for diffusion policy transfer, yielding up to 26% improvement in cross-embodiment block pushing.
Reachability maps don't have to trade off precision, speed, and flexibility: RichMap achieves all three.
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 $渭$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.
MIT CSAIL