Diagonalized Lagrangian robot dynamics

Abstract

A diagonal equation for robot dynamics is developed by combining mass matrix factorization results with classical Lagrangian mechanics. Diagonalization implies that at each fixed 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 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. The total rate at a given joint k reflects the total rotational velocity about the joint, and includes the combined effects from all the links between joint k and the base. Similarly, the working moments are related to the applied moments by the spatial operator . The working moment at a given joint is that part of the applied moment which does actual mechanical work. The diagonal equations are obtained by using the mass matrix factorization in the system Lagrangian.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>