Spatial operator factorization and inversion of the manipulator mass matrix

Abstract-’bo new recursive factorizations are developed of the mass matrix for fixed-base and mobile-base manipulators. First, the mass matrix M is shown to have the factorization M = H$M$ * H’. This is referred to here as the Newton-Euler factorization because it is closely related to the recursive New-ton-Euler equations of motion. This factorization may be the simplest way to show the equivalence of recursive Newton-Euler and Lagrangian manipulator dynamics. Second, the mass matrix is shown to have a related innovations factorization M = (2+ H Q G) D ( Z + H 9 G) *. This leads to an immediate inversion M- ’ = (2- H 4 G) * D-l (Z- H 4 G) , where H and are given by known link geometric parameters, and G, 4 and D are obtained by a discrete-step Riccati equation driven by the link masses. The factors (Z + H 9 G) and (Z- H q G) are lower triangular matrices that are inverses of each other, an