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.

中文翻译：

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互补约束下使用无限程序规划权力掌握

我们提出了一种基于优化的方法来计划力量掌握。我们方法的核心是将抓取规划重新制定为互补约束（IPCC）下的无限程序，它允许在物体和机器人抓手上的任意点对之间发生接触。我们表明可以使用核积分松弛将 IPCC 简化为传统的有限维非线性程序 (NLP)。此外，核积分的值和雅可比矩阵可以使用改进的快速多极方法 (FMM) 进行有效评估。我们使用原始障碍惩罚进一步保证计划的抓取是无碰撞的。我们在一系列具有挑战性的 3D 对象和高自由度抓手（例如 Barrett Hand 和 Shadow Hand）上展示了我们的抓取规划器的有效性、稳健性和效率，