New Formulation of Mixed-Integer Conic Programming for Globally Optimal Grasp Planning
This work addresses grasp planning for robotics, offering improved optimality but with incremental computational advances.
The paper tackles the problem of globally optimal grasp planning by introducing a two-level branch-and-bound algorithm that maximizes a grasp metric while considering gripper kinematics feasibility, resulting in computation times of 20-180 minutes and better grasp quality compared to sampling-based planners.
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.