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

2026-04-08

AI Summary

This work addresses the challenge of achieving high precision, computational efficiency, and structural flexibility simultaneously in reachability maps for complex robotic manipulation. We propose RichMap, a novel reachability map representation that enhances grid-based structures to approximate the performance of compact maps while preserving adaptability, enabling both efficient construction and querying. Our approach introduces several key innovations: a coverage guarantee mechanism grounded in theoretical capacity bounds over 𝕊² (or SO(3)), an asynchronous construction pipeline, a maximum mean discrepancy (MMD)-based workspace similarity metric, and an energy-guided cross-embodiment diffusion policy transfer strategy. Experimental results demonstrate that RichMap achieves over 98% prediction accuracy, a false positive rate of only 1–2%, and batch query speeds of approximately 15 microseconds per query, while improving cross-embodiment policy transfer success by 26% in block-pushing tasks.

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 $μ$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.

Problem

• reachability map
• robot manipulation
• efficiency
• flexibility
• precision

Innovation

• Reachability Map
• SO(3) Coverage
• Asynchronous Construction
• Diffusion Policy Transfer
• Workspace Similarity