Certified grasping

Abstract

This thesis studies the notion of robustness on the planar grasping problem, 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. This work develops convex-combinatorial models for each of these certificates, which can be expressed as simple semi-algebraic relations under mild-modeling assumptions on the object and robot shapes. 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, as well as its underlying models, with simulations and real robot experiments, by caging and grasping random polygons, comparing against other standard grasp planning algorithms, and performing sensorless grasps over different objects.