A recursive Newton-Euler algorithm for robots with elastic joints and its application to control

We consider the problem of computing the inverse dynamics of a serial robot manipulator with N elastic joints in a recursive numerical way. The solution algorithm is a generalized version of the standard Newton-Euler approach, running still with linear complexity O(N) but requiring to set up recursions that involve higher order derivatives of motion and force variables. Mimicking the case of rigid robots, we use this algorithm and a numerical factorization of the link inertia matrix (which needs to be inverted in the elastic joint case) for implementing on-line a feedback linearization control law for trajectory tracking purposes. The complete method has a complexity that grows as O(N³). The developed tools are generic, easy to use, and do not require symbolic Lagrangian modeling and customization, thus being of particular interest when the number N of elastic joints becomes large.