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Point set registration is a powerful method that enables robots to manipulatedeformable objects. By mapping the point cloud of the current object to thepre-trained point cloud, a transformation function can be constructed. Themanipulator's trajectory for pre-trained shapes can be warped with thistransformation function, yielding a feasible trajectory for the new shape.However, usually this transformation function regards objects as discretepoints, and dismisses the topological structures. Therefore, it risksover-stretching or over-compression during manipulation. To tackle thisproblem, this paper proposes a tangent space point set registration method. Atangent space representation of an object is constructed by defining an anglefor each node on the object. Point set registration algorithm runs in thisnewly-constructed tangent space, yielding a tangent space trajectory. Thetrajectory is then converted back to Cartesian space and carried out by therobot. Compared to its counterpart in Cartesian space, tangent space point setregistration is safer and more robust, succeeding in a series of experimentssuch as rope straightening, rope knotting, cloth folding and unfolding.

Learn the Manipulation of Deformable Objects Using Tangent Space Point Set Registration