Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact topological representations to capture the state of highly deformable objects that are topologically nontrivial. We develop an approach that tracks the evolution of this topological state through time. Under several mild assumptions, we prove that the topology of the scene and its evolution can be recovered from point clouds representing the scene. Our further contribution is a method to learn predictive models that take a sequence of past point cloud observations as input and predict a sequence of topological states, conditioned on target/future control actions. Our experiments with highly deformable objects in simulation show that the proposed multistep predictive models yield more precise results than those obtained from computational topology libraries. These models can leverage patterns inferred across various objects and offer fast multistep predictions suitable for real-time applications.

中文翻译：

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变形对象预测模型的顺序拓扑表示

由于缺少规范的低维表示以及难以捕获，预测和控制此类对象，因此可变形对象给机器人操作带来了巨大挑战。我们构造紧凑的拓扑表示形式，以捕获拓扑上无关紧要的高度可变形对象的状态。我们开发了一种方法来跟踪这种拓扑状态随时间的演变。在几个温和的假设下，我们证明了场景的拓扑及其演化可以从代表场景的点云中恢复。我们的进一步贡献是一种学习预测模型的方法，该模型将一系列过去的点云观测作为输入并根据目标/未来控制动作预测一系列拓扑状态。我们在仿真中对高度变形的对象进行的实验表明，与从计算拓扑库获得的结果相比，提出的多步预测模型产生的结果更精确。这些模型可以利用跨各种对象推断出的模式，并提供适用于实时应用的快速多步预测。