  We propose an optimization-based approach to plan power grasps. Central to
our method is a reformulation of grasp planning as an infinite program under
complementary constraints (IPCC), which allows contacts to happen between
arbitrary pairs of points on the object and the robot gripper. We show that
IPCC can be reduced to a conventional finite-dimensional nonlinear program
(NLP) using a kernel-integral relaxation. Moreover, the values and Jacobian
matrices of the kernel-integral can be evaluated efficiently using a modified
Fast Multipole Method (FMM). We further guarantee that the planned grasps are
collision-free using primal barrier penalties. We demonstrate the
effectiveness, robustness, and efficiency of our grasp planner on a row of
challenging 3D objects and high-DOF grippers, such as Barrett Hand and Shadow
Hand, where our method achieves superior grasp qualities over competitors.
