提出一种高精度、高效灵活的机器人操作可达性地图，支持复杂任务规划。
RichMap: A Reachability Map Balancing Precision, Efficiency, and Flexibility for Rich Robot Manipulation Tasks
- 基于网格结构优化，结合球面容量理论保证覆盖精度
- 预测准确率超98%，单次查询仅需约15微秒，误报率1%~2%
- 适用于跨体态迁移和工作空间相似性评估，适合复杂操作任务
本文提出RichMap，一种高精度的可达性地图表示方法，旨在平衡机器人多样化操作任务中的效率与灵活性。通过改进经典网格结构，提出一种简化方案，在性能上接近紧凑型地图（如RM4D）的同时保持结构灵活性。方法利用$/mathbb{S}^2$（或$SO(3)$）上的理论容量界限确保严格覆盖，并采用异步流水线实现高效构建。在综合指标下验证了该地图：预测准确率超过98%，假阳性率维持在1%~2%，大规模批量查询速度达约15 μs/查询。进一步拓展应用，通过最大均值差异（MMD）量化机器人工作空间相似性，并在扩散策略迁移中引入能量引导，块推实验中跨体态场景性能提升最高达26%。
原文摘要 · Abstract (English)
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.
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