用流形结构统一处理接触规划，实现快速精准操作。
Contact Modes Are Strata: What Geometric Structure Buys in Discrete-Continuous Planning
- 将接触模式视为配置空间的流形层，显式建模运动约束
- 在模拟中两任务均秒级求解，无需预设接触序列
- 适合高精度抓取与复杂环境下的机器人操作研究
接触丰富的操作同时涉及离散选择（哪些接触存在）和连续规划（如何移动）。两者通过维数变化耦合：每个维持的接触将机器人的运动限制在更低维的流形上。本文提出将接触模式直接视为配置空间的流形层，使规划变为在流形层间移动，层内路径为测地线。在两个模拟任务中——推动T型块绕障碍物、灵巧手重定向立方体——该规划器在无预先给定模式、接触序列或流形的情况下，均能在数秒内返回可行解。
原文摘要 · Abstract (English)
Contact-rich manipulation poses a discrete question and a continuous one at once, namely which contacts are active and how to move while they hold. The two are coupled by a change of dimension, since each contact that a robot maintains confines its motion to a lower-dimensional manifold. We make that coupling the explicit object of planning by observing that a contact mode is not merely analogous to a stratum of the configuration space; it is one. A plan is then a walk over strata whose within-stratum segments are geodesics. On two contact-rich manipulation tasks in simulation, pushing a T-shaped block around obstacles and reorienting a cube in a dexterous hand, our planner returns solutions within seconds with no mode, contact sequence, or stratum given in advance.
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