A computationally efficient method for modeling flexible robots based on the assumed modes method

In this paper a simple method to obtain the analytical model of a flexible robot is presented, which turns out to be more efficient, from a computational point of view, than the classic assumed modes method.The presented method consists of using appropriate linear combinations of the modes of each link as basis functions to evaluate the deflection, in such a way as to minimize the dependency of the position of the generic link on the Lagrangian variables of the previous links. Hence, the number of terms of the inertia matrix and of the Coriolis and centrifugal vectors is significantly reduced. First, the model is derived, provided that the links are homogeneous and with constant cross-section, by analytically or otherwise by numerically calculating the parameters of the closed-form expression of the Lagrangian function of the generic link supposed free; afterwards, the analytical dynamic model of the whole robot is obtained by using an iterative interconnection algorithm, which can be easily implemented by using a symbolic manipulation language.The simplicity and efficiency of the proposed method is illustrated by considering the analytic expression of the kinetic energy of the end-effector in different cases and with significant comparison examples.