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Planning long-horizon robot manipulation requires making discrete decisions about which objects to interact with and continuous decisions about how to interact with them. A robot planner must select grasps, placements, and motions that are feasible and safe. This class of problems falls under Task and Motion Planning (TAMP) and poses significant computational challenges in terms of algorithm runtime and solution quality, particularly when the solution space is highly constrained. To address these challenges, we propose a new bilevel TAMP algorithm that leverages GPU parallelism to efficiently explore thousands of candidate continuous solutions simultaneously. Our approach uses GPU parallelism to sample an initial batch of solution seeds for a plan skeleton and to apply differentiable optimization on this batch to satisfy plan constraints and minimize solution cost with respect to soft objectives. We demonstrate that our algorithm can effectively solve highly constrained problems with non-convex constraints in just seconds, substantially outperforming serial TAMP approaches, and validate our approach on multiple realworld robots. 

Shape servoing, a robotic task dedicated to controlling objects to desired goal shapes, is a promising approach to deformable object manipulation. An issue arises, however, with the reliance on the specification of a goal shape. This goal has been obtained either by a laborious domain knowledge engineering process or by manually manipulating the object into the desired shape and capturing the goal shape at that specific moment, both of which are impractical in various robotic applications. In this paper, we solve this problem by developing a novel neural network DefGoalNet, which learns deformable object goal shapes directly from a small number of human demonstrations. We demonstrate our method’s effectiveness on various robotic tasks, both in simulation and on a physical robot. Notably, in the surgical retraction task, even when trained with as few as 10 demonstrations, our method achieves a median success percentage of nearly 90%. These results mark a substantial advancement in enabling shape servoing methods to bring deformable object manipulation closer to practical real-world applications.