Certified grasping

This paper studies the robustness of grasping in the frictionless plane from a geometric perspective. By treating grasping as a process that shapes the free-space object over time, we define three types of certificates to guarantee success of a grasp: (a) invariance under an initial set, (b) convergence toward a goal grasp, and (c) observability over the final object pose. We develop convex-combinatorial models for each of these certificates, which can be expressed as simple semi-algebraic relations under mild-modeling assumptions, such as point-fingers and frictionless contact. By leveraging these models to synthesize certificates, we optimize certifiable grasps of planar objects composed as a union of convex polygons, using manipulators described as point-fingers. We validate this approach in simulations by grasping random polygons, and with real sensorless grasps of several objects.