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arXiv · 1909.05430

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

Min Liu·Zherong Pan·Kai Xu·Dinesh Manocha
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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 Q1 metric, is better than those generated using sampling-based planners.

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Min Liu, Zherong Pan, Kai Xu, Dinesh Manocha. 2019-09-12. New Formulation of Mixed-Integer Conic Programming for Globally Optimal Grasp Planning. https://arxiv.org/abs/1909.05430

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