Grasp Moduli Spaces

Abstract

Abstract-We present a new approach for modelling grasping using an integrated space of grasps and shapes. In particular, we introduce an infinite dimensional space, the Grasp Moduli Space, which represents shapes and grasps in a continuous manner. We define a metric on this space allowing us to formalize 'nearby' grasp/shape configurations and we discuss continuous deformations of such configurations. We work in particular with surfaces with cylindrical coordinates and analyse the stability of a popular L 1 grasp quality measure Q l under continuous deformations of shapes and grasps. We experimentally determine bounds on the maximal change of Q l in a small neighbourhood around stable grasps with grasp quality above a threshold. In the case of surfaces of revolution, we determine stable grasps which correspond to grasps used by humans and develop an efficient algorithm for generating those grasps in the case of three contact points. We show that sufficiently stable grasps stay stable under small deformations. For larger deformations, we develop a gradient-based method that can transfer stable grasps between different surfaces. Additionally, we show in experiments that our gradient method can be used to find stable grasps on arbitrary surfaces with cylindrical coordinates by deforming such surfaces towards a corresponding 'canonical' surface of revolution.

Grasp moduli spaces and spherical harmonics

“…Furthermore, while previously objects such as boxes, cylinders, spheres and quadric surfaces have been considered as primitives for the purpose of grasping and manipulation (see [1] and references therein), we shall argue that shape primitives defined in terms of a spectral analysis of the underlying objects provides a useful alternative. Our work extends the approach of [2], where an infinite dimensional space -the Grasp Moduli Space -for contact configurations on surfaces parametrized by a cylindrical coordinate chart was introduced. It was shown that shape deformation based approaches in this space can be used to synthesize and transfer stable grasps if a smooth surface representation of the object is known.…”

“…In this work, we utilize a spectral object representation, which has also recently been used in neuroanatomy [3], and show how such a representation can form a basis for a deformation based grasp synthesis framework. Our present work extends the approach of [2] since it allows us to use point cloud data directly. Furthermore, grasps on any genus zero (i.e.…”

“…Our approach is instead based on a smooth object parametrization and extends the work of [2], where the space of surfaces with cylindrical coordinates, M cyl , was considered. The space M cyl is convex, allowing us to deform between any two surfaces S 1 , S 2 using a curve γ :…”

“…, S n } induces a finite dimensional shape subset Conv(X) consisting of convex combinations of elements of X. In [2], this shape space is combined with a space of configurations of contact points to define a Grasp Moduli Space G cyl parametrizing both a shape and a set of contact points on the shape. A metric on G cyl can then be defined and one can continuously move between any two points in G cyl .…”

Category-based task specific grasping

“…Recently, Pokorny et al in [18,19] present an infinite dimensional space-the Grasp Moduli Space, which combines grasps and objects parametrized by smooth differentiable functions. In this space various surface/grasp configurations can be continuously deformed in order to synthesize force closed grasps on novel objects.…”