FRoGGeR

Overview

We propose a differentiable, analytic grasp metric that enables collision-free grasp synthesis for dexterous hands in seconds (vs. minutes for existing methods). Our grasp metric is a relaxation of the feasibility LP traditionally used to check if a grasp is in “force closure:”

\[\begin{aligned} \ell^*(q) = \max_{\alpha \in \mathbb{R}^m, \; \ell \in \mathbb{R}} & \quad \ell \\ \text{s.t.} & \quad W(q) \alpha = 0\\ & \quad \mathbf{1}^T \alpha = 1 \\ & \quad \alpha \geq \ell \mathbf{1} \end{aligned}\]

We show empirically that optimizing our metric yields robust grasps and it is well-correlated with existing metrics.

Using results from differentiable optimization, we can compute gradients of our metric \(\ell^*(q)\) with respect to the hand configuration \(q\) in fractions of a millisecond. This allows us to quickly generate diverse, collision-free grasps using nonlinear programming.

Our method for grasp generation, FRoGGeR, can be used to quickly post-process grasps generated from both simple heuristics and learning-based generative models, and has exciting applications for both real-time grasp planning and for generating grasp data at scale for training learning-based models.