New Formulation of Mixed-Integer Conic Programming for Globally Optimal Grasp Planning
Min Liu, Zherong Pan, Kai Xu, Dinesh Manocha
Abstract
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 Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> metric, is better than those generated using sampling-based planners.
BibTeX
@inproceedings{ral2020_newformulationof,
title = {New Formulation of Mixed-Integer Conic Programming for Globally Optimal Grasp Planning},
author = {Min Liu and Zherong Pan and Kai Xu and Dinesh Manocha},
booktitle = {RA-L 2020},
year = {2020}
}