The UDU/sup T/ decomposition of manipulator inertia matrix

In this paper the UDU/sup 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/sup 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.