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We present a two-level branch-and-bound (BB) algorithm to compute the optimalgripper pose that maximizes a grasp metric in a restricted search space. Ourmethod can take the gripper's kinematics feasibility into consideration toensure that a given gripper can reach the set of grasp points withoutcollisions or predict infeasibility with finite-time termination when no poseexists for a given set of grasp points. Our main technical contribution is anovel mixed-integer conic programming (MICP) formulation for the inversekinematics of the gripper that uses a small number of binary variables andtightened constraints, which can be efficiently solved via a low-level BBalgorithm. Our experiments show that optimal gripper poses for various targetobjects can be computed taking 20-180 minutes of computation on a desktopmachine and the computed grasp quality, in terms of the Q1 metric, is betterthan those generated using sampling-based planners.

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