# Certified Grasping

arXiv: https://arxiv.org/abs/1909.03985 · HTML: https://mlsanity.com/paper/1909.03985/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2019.

## Built on by (most cited first, 3 of 3)

- [Dynamics-Guided Diffusion Model for Sensor-less Robot Manipulator Design](https://mlsanity.com/paper/2402.15038/) (2024)
- [A Differentiable Recipe for Learning Visual Non-Prehensile Planar Manipulation](https://mlsanity.com/paper/2111.05318/) (2021)
- [Physics-Informed Eikonal Caging for Whole-Arm Manipulation Planning](https://mlsanity.com/paper/2606.22143/) (2026)

## Abstract (arXiv)

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.