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

摘要

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