A NEW O(N) METHOD FOR INVERTING THE MASS MATRIX FOR SERIAL CHAINS COMPOSED OF RIGID BODIES

摘要

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. In this paper, a method developed in 1973 by Fixman for O(n) computation of the mass-matrix determinant for a polymer chain consisting of point masses is adapted and modified. In other recent papers, we and our collaborators recently extended this method in order for Fixman's results to be applicable to robotic manipulator models with lumped masses. In the present paper we extend these ideas further to 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 how to differentiate functions of group-valued argument.