Robotic Manipulation of Deformable Objects by Tangent Space Mapping and Non-Rigid Registration

Recent works of non-rigid registration have shown promising applications on tasks of deformable manipulation. Those approaches use thin plate spline-robust point matching (TPS-RPM) algorithm to regress a transformation function, which could generate a corresponding manipulation trajectory given a new pose/shape of the object. However, this method regards the object as a bunch of discrete and independent points. Structural information, such as shape and length, is lost during the transformation. This limitation makes the object's final shape to differ from training to test, and can sometimes cause damage to the object because of excessive stretching. To deal with these problems, this paper introduces a tangent space mapping (TSM) algorithm, which maps the deformable object in the tangent space instead of the Cartesian space to maintain structural information. The new algorithm is shown to be robust to the changes in the object's pose/shape, and the object's final shape is similar to that of training. It is also guaranteed not to overstretch the object during manipulation. A series of rope manipulation tests are performed to validate the effectiveness of the proposed algorithm.