# New Formulation of Mixed-Integer Conic Programming for Globally Optimal Grasp Planning

arXiv: https://arxiv.org/abs/1909.05430 · HTML: https://mlsanity.com/paper/1909.05430/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 1 of 1)

- [Learning High-DOF Reaching-and-Grasping via Dynamic Representation of Gripper-Object Interaction](https://mlsanity.com/paper/2204.13998/) (2022)

## Abstract (arXiv)

We present a two-level branch-and-bound (BB) algorithm to compute the optimal gripper pose that maximizes a grasp metric in a restricted search space. Our method can take the gripper's kinematics feasibility into consideration to ensure that a given gripper can reach the set of grasp points without collisions or predict infeasibility with finite-time termination when no pose exists for a given set of grasp points. Our main technical contribution is a novel mixed-integer conic programming (MICP) formulation for the inverse kinematics of the gripper that uses a small number of binary variables and tightened constraints, which can be efficiently solved via a low-level BB algorithm. Our experiments show that optimal gripper poses for various target objects can be computed taking 20-180 minutes of computation on a desktop machine and the computed grasp quality, in terms of the Q1 metric, is better than those generated using sampling-based planners.