Penalty-based Numerical Representation of Rigid Body Interactions with Applications to Simulation of Robotic Grasping

This paper presents a novel approach to numerically describe interactions between rigid bodies, with a special focus on robotic grasping. Some of the more common approaches used to represent such interactions 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 configu-rations 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 in simulation. This is pursued through the use of a penalty-based approach, and draws on notions of mechani-cal impedance to infer apposite reaction forces that allows to overcome well established limitations of classical penalty-based approaches. Results of numerical simulations illustrate efficacy of the proposed approach.