Diagonalized Lagrangian Robot Dynamics

A diagonal equation _ + C(;) = for robot dynamics is developed by combining recent mass matrix factorization results [1{7] with classical Lagrangian mechanics. Diagonalization im-plies that at each xed time instant the equation at each joint is decoupled from all of the other joint equations. The equation involves two important variables: a vector of total joint rotational rates and a corresponding vector of working joint moments. The nonlinear Coriolis term C(;) depends on the joint angles and the rates . The total joint rates are related to the relative joint-angle rates _ by a linear spatial operator m () mechanized by a base-to-tip spatially recursive algorithm. The total rate (k) at a given joint k re ects, in a very unique sense the total rotational velocity about the joint, and includes the combined eects from all the links between joint k an