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.
Results
Grasp Optimzation
We study FRoGGeR’s performance on over 40 objects drawn from the YCB dataset, outperforming a competitive baseline in computation time, feasibility rate of grasp synthesis, and picking success in simulation. We conclude that FRoGGeR is fast: it has a median synthesis time of 0.834s over hundreds of experiments.
Comparison with Ferrari-Canny
We also study how our proposed metric \(\ell^*(q)\) correlates with existing metrics for grasp quality. We find that our metric is well-correlated with the traditional \(\epsilon\)-ball (or “Ferrari-Canny”) grasp metric, a standard robustness measure for dexterous grasping.
Citing
If you find this work useful in your research, please cite:
@article{
li2023_frogger,
title={FRoGGeR: Fast Robust Grasp Generation via the Min-Weight Metric},
author={Albert H. Li and Preston Culbertson and Joel W. Burdick and Aaron D. Ames},
journal={arxiv:2302.13687},
month={February},
year={2023},
}