The UDUT decomposition of manipulator inertia matrix

In this paper the UDU^T decomposition of the generalized inertia matrix of an n-link serial manipulator as presented in symbolic form, where U and D, respectively, are the upper triangular and diagonal matrices. To render the decomposition, the elementary upper triangular matrices, associated to a modified Gaussian elimination, are introduced, whereas each element of the inertia matrix is written as an expression, instead of finding it as a number with the aid of an algorithm. The resulting UDU^T decomposition shows recursive relations among the elements of the associated matrices. Thus, algorithms of order `n´ can be developed not only for the inverse but also for the forward dynamics. As an illustration, a forward dynamics algorithm is presented here