Efficient computation of articulated-body inertias using successive axial screws

The articulated-body (AB) algorithm for dynamic simulation of chains of rigid bodies was developed by Featherstone (1983). The mast costly step in this algorithm is the computation of the AB inertias at each link which involves a spatial (6×6) congruence transformation. The amount of computation required is closely coupled to the kinematic modeling technique used. This paper examines this computation in detail and presents an efficient step-by-step procedure for its evaluation in a serial chain with revolute and prismatic joints using modified Denavit-Hartenberg parameters for modeling the kinematics. The result is a very efficient procedure using successive axial screws that reduces the computational requirements of the AB algorithm by about 15% from results obtained by Brandl, Johanni, and Otter (1986). The procedure developed defines a general approach and can be used to improve the efficiency of spatial congruence transformations of other types of matrices, such as spatial rigid-body inertias (used in the composite rigid-body simulation algorithm)