O(n) mass matrix inversion for serial manipulators and polypeptide chains using Lie derivatives

Over the past several decades, a number of O(n) methods for forward and inverse dynamics computations have been developed in the multibody dynamics and robotics literature. A method was developed by Fixman in 1974 for O(n) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other of our recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and specifically, it requires that one differentiates real-valued functions of Liegroup-valued argument.