On computing real logarithms for matrices in the Lie group of special Euclidean motions in Rn

Abstract

We show that the diagonal Pade approximants methods, both for computing the principal logarithm of matrices belonging to the Lie groupSE (n, IR) of special Euclidean motions in IRn and to compute the matrix exponential of elements in the corresponding Lie algebra se(n, IR), are structure preserving. Also, for the particular cases when n == 2,3 we present an alternative closed form to compute the principal logarithm. These low dimensional Lie groups play an important role in the kinematic motion of many mechanical systems and, for that reason, the results presented here have immediate applications in robotics