On the Equivalence of Lagrangian and Newton-Euler Dynamics for Manipulators

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Abstract
Recently, there has been considerable interest in efficient formulations of manipulator dynamics. The inefficiency of the classic Lagrangian formulation is well known, leading several researchers to a new formulation based on the Newton-Euler equations. This formulation is highly ef ficient, but 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 formula tion is due to two factors: the recursive structure of the computation and the representation chosen for the rota tional dynamics. Both of these factors can be achieved in a Lagrangian formulation. Recursive Lagrangian dy namics has been discussed previously by Hollerbach. This paper compares the representations that have been used and shows that with a proper choice the Lagrangian formulation is indeed equivalent to the Newton-Euler formulation.

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