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Deformable objects present a formidable challenge for robotic manipulationdue to the lack of canonical low-dimensional representations and the difficultyof capturing, predicting, and controlling such objects. We construct compacttopological representations to capture the state of highly deformable objectsthat are topologically nontrivial. We develop an approach that tracks theevolution of this topological state through time. Under several mildassumptions, we prove that the topology of the scene and its evolution can berecovered from point clouds representing the scene. Our further contribution isa method to learn predictive models that take a sequence of past point cloudobservations as input and predict a sequence of topological states, conditionedon target/future control actions. Our experiments with highly deformableobjects in simulation show that the proposed multistep predictive models yieldmore precise results than those obtained from computational topology libraries.These models can leverage patterns inferred across various objects and offerfast multistep predictions suitable for real-time applications.

Sequential Topological Representations for Predictive Models of Deformable Objects