Certified Grasping

This paper studies robustness in planar grasping from a geometric perspective. By treating grasping as a process that shapes the free-space of an object over time, we can define three types of certificates to guarantee success of a grasp: (a) invariance under an initial set, (b) convergence towards 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. By leveraging these models to synthesize certificates, we optimize certifiable grasps of arbitrary planar objects composed as a union of convex polygons, using manipulators described as point-fingers. We validate this approach with simulations and real robot experiments, by grasping random polygons, comparing against other standard grasp planning algorithms, and performing sensorless grasps over different objects.