Applications in fields ranging from home care to warehouse fulfillment to surgical assistance require robots to reliably manipulate the shape of 3D deformable objects. 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 manipulated object 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 a visual servo controller that computes the desired robot end-effector action to iteratively deform the object toward the target shape. We demonstrate both in simulation and on a physical robot that DeformerNet reliably generalizes to object shapes and material stiffness not seen during training. Crucially, using DeformerNet, the robot successfully accomplishes three surgical sub-tasks: retraction (moving tissue aside to access a site underneath it), tissue wrapping (a sub-task in procedures like aortic stent placements), and connecting two tubular pieces of tissue (a sub-task in anastomosis).

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