Stability of Second-Order Asymmetric Linear Mechanical Systems With Application to Robot Grasping

Abstract

This technical correspondence presents a surprisingly simple analytical criterion for the stability of general second-order asymmetric linear systems. The criterion is based on the fact that if a symmetric system is stable, adding a small amount of asymmetry would not cause instability. We compute analytically an upper bound on the allowed asymmetry such that the overall linear system is stable. This stability criterion is then applied to robot grasping arrangements which, due to physical effects at the contacts, are asymmetric mechanical systems. We present an application of the stability criterion to a 2D grasp arrangement.