Numerical stability of forward-dynamics algorithms

Many physical systems, particularly robotic linkages, can be modeled as mechanisms. In order to simulate the dynamical behavior of such systems as the number of links become large, the algorithms must produce efficient and stable computations. The mechanisms studied here include those which have tree-structured topologies, that is, a link may have more than one successor link but there are no loops in the linkage topology. The authors present a formulation of the dynamics based on representing Lagrangian mechanics with spatial, or screw, displacements. This shows that several existing algorithms are equivalent to recursive calculations on an inertial supermatrix, which is a matrix the elements of which are matrices. The result is numerically stable forward and inverse computations of the second-order terms that grow linearly with the number of links, and provides a new insight into the nature of the dynamics of mechanisms