Grasp moduli spaces and spherical harmonics

In this work, we present a novel representation which enables a robot to reason about, transfer and optimize grasps on various objects by representing objects and grasps on them jointly in a common space. In our approach, objects are parametrized using smooth differentiable functions which are obtained from point cloud data via a spectral analysis. We show how, starting with point cloud data of various objects, one can utilize this space consisting of grasps and smooth surfaces in order to continuously deform various surface/grasp configurations with the goal of synthesizing force closed grasps on novel objects. We illustrate the resulting shape space for a collection of real world objects using multidimensional scaling and show that our formulation naturally enables us to use gradient ascent approaches to optimize and simultaneously deform a grasp from a known object towards a novel object.