Recent work [1], [2] has shown promising results in enabling robotic manipulation of deformable objects through learning from demonstrations. Their method computes a registration from training scene to test scene, and then applies an extrapolation of this registration to the training scene gripper motion to obtain the gripper motion for the test scene. The warping cost of scene-to-scene registrations is used to determine the nearest neighbor from a set of training demonstrations. Then once the

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... ripper motion has been generalized to the test situation, they apply trajectory optimization [3] to plan for the robot motions that will track the predicted gripper motions. In many situations, however, the predicted gripper motions cannot be followed perfectly due to, for example, joint limits or obstacles. In this case the past work finds a path that minimizes deviation from the predicted gripper trajectory as measured by its Euclidean distance for position and angular distance for orientation. Measuring the error this way during the motion planning phase, however, ignores the underlying structure of the problem-namely the idea that rigid registrations are preferred to generalize from training scene to test scene. Deviating from the gripper trajectory predicted by the extrapolated registration effectively changes the warp induced by the registration in the part of the space where the gripper trajectories are. The main contribution of this paper is an algorithm that considers this effective final warp as the criterion to optimize for in a unified optimization that simultaneously considers the scene-to-scene warping and the robot trajectory (which were separated into two sequential steps by the past work). This results in an approach that adjusts to infeasibility in a way that adapts directly to the geometry of the scene and minimizes the introduction of additional warping cost. In addition, this paper proposes to learn the motion of the gripper pads, whereas past work considered the motion of a coordinate frame attached to the gripper as a whole. This enables learning more precise grasping motions. Our experiments, which consider the task of knot tying, show that both unified optimization and explicit consideration of gripper pad motion result in improved performance.