This paper presents a novel approach to numerically describe the interactions between rigid bodies, with a special focus on robotic grasping. Some of the more common approaches used to address such issues rely on satisfaction of a set of strict constraints, descriptive of the expected physical reality of such interactions in practice. However, application of constraint-based methods in a numerical setting may lead to problematic configurations in which, for instance, volumes occupied by distinct bodies may overlap. Such situations lying beyond the range of admissible configurations for constraint-based methods, their occurrence typically results in non-meaningful simulation outcomes. We propose a method which acknowledges the possibility of such occurrences while demoting their occurrence. This is pursued through the use of a penalty-based approach, and draws on notions of mechanical impedance to infer apposite reaction forces. Results of numerical simulations illustrate efficacy of the proposed approach.

中文翻译：

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基于惩罚的刚体相互作用的数值表示与机器人抓取仿真的应用

本文提出了一种新的方法来数值描述刚体之间的相互作用，特别关注机器人抓取。用于解决此类问题的一些更常见的方法依赖于一组严格约束的满足，这些约束描述了实践中此类交互的预期物理现实。然而，在数值设置中应用基于约束的方法可能会导致有问题的配置，例如，不同物体占据的体积可能会重叠。这种情况超出了基于约束的方法的允许配置范围，它们的发生通常会导致无意义的模拟结果。我们提出了一种方法，该方法承认此类事件发生的可能性，同时将其降级。这是通过使用基于惩罚的方法来实现的，并利用机械阻抗的概念来推断适当的反作用力。数值模拟的结果说明了所提出方法的有效性。