Manipulation of deformable objects often requires a robot to apply specific forces to bring the object into the desired configuration. For instance, tightening a knot requires pulling on the ends, flattening an article of clothing requires smoothing out wrinkles, and erasing a whiteboard requires applying downward pressure. We present a method for learning force-based manipulation skills from demonstrations. Our approach uses non-rigid registration to compute a warping function that transforms both the end-effector poses and forces in each demonstration into the current scene, based on the configuration of the object. Our method then uses the variation between the demonstrations to extract a single trajectory, along with time-varying feedback gains that determine how much to match poses or forces. This results in a learned variable-impedance control strategy that trades off force and position errors, providing for the right level of compliance that applies the necessary forces at each stage of the motion. We evaluate our approach by tying knots in rope, flattening towels, and erasing a whiteboard.

Learning from demonstration by means of non-rigid point cloud registration is an effective tool for learning to manipulate a wide range of deformable objects. However, most methods that use non-rigid registration to transfer demonstrated trajectories assume that the test and demonstration scene are structurally very similar, with any variation explained by a non-linear transformation. In real-world tasks with clutter and distractor objects, this assumption is unrealistic. In this work, we show that a trajectory-aware non-rigid registration method that uses multiple demonstrations to focus the registration process on points that are relevant to the task can effectively handle significantly greater visual variation than prior methods that are not trajectory-aware. We demonstrate that this approach achieves superior generalization on several challenging tasks, including towel folding and grasping objects in a box containing irrelevant distractors.