将6/7轴机械臂工作空间压缩至4D，实现高效正反向可达性查询
RM4D: A Combined Reachability and Inverse Reachability Map for Common 6-/7-axis Robot Arms by Dimensionality Reduction to 4D
- 通过降维将6维工作空间简化为4维，统一表示正反向可达性
- 构建的RM4D地图比传统方法快10倍以上，精度无损失
- 适合移动操作臂抓取规划，支持快速决策
机械臂工作空间知识对机器人设计、抓取规划和基座定位等任务至关重要。常用的两种表示是可达性地图和逆可达性地图：前者判断当前姿态下末端是否可达，后者为指定末端姿态推荐合适的基座位置。传统方法需在6维空间离散化并逐点判断可达性，再反转生成逆地图，过程繁琐且效率低。本文利用六轴与七轴机械臂的共性，将离散维度从6维降至4维，提出可达性地图4D（RM4D），仅用一个4维数据结构即可支持正向与逆向查询。该方法显著提升构建速度，较现有方案快一个数量级，无需反转开销，且精度不变。实验表明，RM4D在移动操作臂抓取规划中具有实用价值。
原文摘要 · Abstract (English)
Knowledge of a manipulator's workspace is fundamental for a variety of tasks including robot design, grasp planning and robot base placement. Consequently, workspace representations are well studied in robotics. Two important representations are reachability maps and inverse reachability maps. The former predicts whether a given end-effector pose is reachable from where the robot currently is, and the latter suggests suitable base positions for a desired end-effector pose. Typically, the reachability map is built by discretizing the 6D space containing the robot's workspace and determining, for each cell, whether it is reachable or not. The reachability map is subsequently inverted to build the inverse map. This is a cumbersome process which restricts the applications of such maps. In this work, we exploit commonalities of existing six and seven axis robot arms to reduce the dimension of the discretization from 6D to 4D. We propose Reachability Map 4D (RM4D), a map that only requires a single 4D data structure for both forward and inverse queries. This gives a much more compact map that can be constructed by an order of magnitude faster than existing maps, with no inversion overheads and no loss in accuracy. Our experiments showcase the usefulness of RM4D for grasp planning with a mobile manipulator.
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