Point set registration is a powerful method that enables robots to manipulate deformable objects. By mapping the point cloud of the current object to the pre-trained point cloud, a transformation function can be constructed. The manipulator's trajectory for pre-trained shapes can be warped with this transformation function, yielding a feasible trajectory for the new shape. However, usually this transformation function regards objects as discrete points, and dismisses the topological structures. Therefore, it risks over-stretching or over-compression during manipulation. To tackle this problem, this paper proposes a tangent space point set registration method. A tangent space representation of an object is constructed by defining an angle for each node on the object. Point set registration algorithm runs in this newly-constructed tangent space, yielding a tangent space trajectory. The trajectory is then converted back to Cartesian space and carried out by the robot. Compared to its counterpart in Cartesian space, tangent space point set registration is safer and more robust, succeeding in a series of experiments such as rope straightening, rope knotting, cloth folding and unfolding.
To enhance the robotic manipulation of deformable objects, a robust state estimator is proposed to track the object configuration in real time. A Gaussian mixture model (GMM) is constructed to register the object nodes towards the noisy point cloud. To deal with occlusion, the coherent point drift (CPD) regularization is applied on the mixture model, so as to maintain the topological structure from previous sequences of data and to infer the object states in occluded area. The state estimation is further refined by running a dynamic simulation in parallel, which guarantees the estimates to satisfy the object's physical constraints. A series of rope tracking experiments are performed to evaluate the proposed state estimator. It is shown that the object can be tracked robustly with sensor noise, outliers and massive occlusion. We consider the problem of teaching robots by demonstration how to perform manipulation tasks, in which the geometry (including size, shape, and pose) of the relevant objects varies from trial to trial. We present a method, which we call trajectory transfer, for adapting a demonstrated trajectory from the geometry at training time to the geometry at test time. Trajectory transfer is based on non-rigid registration, which computes a smooth transformation from the training scene onto the testing scene. We then show how to perform a multi-step task by repeatedly looking up the nearest demonstration and then applying trajectory transfer. As our main experimental validation, we enable a PR2 robot to autonomously tie five different types of knots in rope. 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 gripper 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. 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. 