Correlation between diagonal ratio and condition number of the generalized inertia matrix of a serial-chain

Abstract

The condition number of the Generalized Inertia Matrix (GIM) of a serial chain can be used to measure its ill-conditioning. However, computation of the condition number is computationally very expensive. Therefore, this paper investigates alternative means to estimate the condition number, in particular, for a very long serial-chain. For this, the diagonal elements of the GIM are examined. It is found that the ratio of the largest and smallest diagonal elements of the GIM, when scaled using an initial estimate of the condition number, closely resembles the condition number. This significantly simplifies the process of detecting ill-conditioning of the GIM, which may help to decide on stability of the system at hand.