Planning of Power Grasps Using Infinite Program Under Complementary Constraints

TL;DR

This paper introduces an optimization-based method for planning power grasps using an infinite program formulation under complementary constraints, enabling flexible contact modeling and efficient computation.

Contribution

It presents a novel reformulation of grasp planning as an infinite program under complementary constraints and reduces it to a finite nonlinear program with efficient evaluation techniques.

Findings

Achieves superior grasp qualities compared to competitors.

Demonstrates robustness and efficiency on complex 3D objects.

Ensures collision-free grasps with primal barrier penalties.

Abstract

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.