Standard and diagonalized Lagrangian dynamics: a comparison

Compares standard and diagonalized Lagrangian robot dynamics equations. This comparison is motivated by diagonalized equations of motion for multibody open kinematic chains with N degrees of freedom. These equations are derived by making use of new joint velocity variables, ν, which can be viewed as time-derivative of Lagrangian quasi-coordinates, similar to those of classical mechanics. A detailed computational complexity analysis of the standard and diagonalized Lagrangian robot dynamics algorithms is discussed in the paper. The results have been compared with those existing in the robotics literature. The author has conducted extensive numerical studies on diagonalized equations of motion and tried to establish some level of confidence with existing methods for dynamics calculations