On the Representation of Angular Velocity and Its Effect on the Efficiency of Manipulator Dynamics Computation

Recently there has been considerable interest in efficient formulations of manipulator dynamics, mostly due to the desirability of real-time control or analysis of physical devices using modest computers. The inefficiency of the classical Lagrangian formulation is well known, and this has led researchers to seek alternative methods. Several authors have developed a highly efficient formulation of manipulator dynamics based on the Newton-Euler equations, and there may be some confusion as to the source of this efficiency. This paper shows that there is in fact no fundamental difference in computational efficiency between Lagrangian and Newton-Euler formulations. The efficiency of the above-mentioned Newton-Euler formulation is due to two factors: the recursive structure of the computation and the representation chosen of the rotational dynamics. Both of these factors can be achieved in the Lagrangian formulation, resulting in an algorithm identical to the Newton-Euler formulation. Recursive Lagrangian dynamics has been discussed previously by Hollerbach. This paper takes the final step by comparing in detail the representations that have been used for rotational dynamics and showing that with a proper choice of representation the Lagrangian formulation is indeed equivalent to the Newton-Euler formulation