Deformable object manipulation (DOM) with point clouds has great potential as non-rigid 3D shapes can be measured without detecting and tracking image features. However, robotic shape control of deformable objects with point clouds is challenging due to: the unknown point-wise correspondences and the noisy partial observability of raw point clouds; the modeling difficulties of the relationship between point clouds and robot motions. To tackle these challenges, this paper introduces a novel modal-graph framework for the model-free shape servoing of deformable objects with raw point clouds. Unlike the existing works studying the object's geometry structure, our method builds a low-frequency deformation structure for the DOM system, which is robust to the measurement irregularities. The built modal representation and graph structure enable us to directly extract low-dimensional deformation features from raw point clouds. Such extraction requires no extra point processing of registrations, refinements, and occlusion removal. Moreover, to shape the object using the extracted features, we design an adaptive robust controller which is proved to be input-to-state stable (ISS) without offline learning or identifying both the physical and geometric object models. Extensive simulations and experiments are conducted to validate the effectiveness of our method for linear, planar, tubular, and solid objects under different settings.

If robots could reliably manipulate the shape of 3D deformable objects, they could find applications in fields ranging from home care to warehouse fulfillment to surgical assistance. Analytic models of elastic, 3D deformable objects require numerous parameters to describe the potentially infinite degrees of freedom present in determining the object's shape. Previous attempts at performing 3D shape control rely on hand-crafted features to represent the object shape and require training of object-specific control models. We overcome these issues through the use of our novel DeformerNet neural network architecture, which operates on a partial-view point cloud of the object being manipulated and a point cloud of the goal shape to learn a low-dimensional representation of the object shape. This shape embedding enables the robot to learn to define a visual servo controller that provides Cartesian pose changes to the robot end-effector causing the object to deform towards its target shape. Crucially, we demonstrate both in simulation and on a physical robot that DeformerNet reliably generalizes to object shapes and material stiffness not seen during training and outperforms comparison methods for both the generic shape control and the surgical task of retraction.

In this paper, we propose a novel approach to 3D deformable object manipulation leveraging a deep neural network called DeformerNet. Controlling the shape of a 3D object requires an effective state representation that can capture the full 3D geometry of the object. Current methods work around this problem by defining a set of feature points on the object or only deforming the object in 2D image space, which does not truly address the 3D shape control problem. Instead, we explicitly use 3D point clouds as the state representation and apply Convolutional Neural Network on point clouds to learn the 3D features. These features are then mapped to the robot end-effector's position using a fully-connected neural network. Once trained in an end-to-end fashion, DeformerNet directly maps the current point cloud of a deformable object, as well as a target point cloud shape, to the desired displacement in robot gripper position. In addition, we investigate the problem of predicting the manipulation point location given the initial and goal shape of the object.