An Innovative Method to Modeling Realistic Flexible Robots

In this paper a modular, computationally efficient and numerically stable method is presented, which allows to obtain the dynamic model of a robot constituted by flexible links having varying cross-section and subjected to generic ending forces and torques and to the gravity actions. This method is based on the use of admissible deformation functions of wavelet type, obtained by using the Instantaneity Principle of the deflection of an element, and on the Euler-Bernoulli beam theory if the link is slender or, otherwise, on the Timoshenko one. Moreover, it is easy to extend the presented methodology to deal also with the case of large link deformations. The kinematic model of the generic link is obtained by using absolute motion and relative deformation coordinates; the dynamic model, derived with the Lagrangian approach, is obtained by assembling the dynamic models of the links by using a recursive algorithm based on the congruence technique. The proposed modeling methodology guarantees no static error independently of the number of wavelet functions per link, both in the presence of generic forces and torques at both ends, for generic cross-section profiles, and in the presence of gravity actions, for several cross-section ones; moreover, it guarantees good dynamic performance in a frequency range which increases when the number of wavelet functions increases. It is shown that the presented methodology is also more efficient and numerically stable than other modeling methods known in literature. This methodology can be used for the dynamic simulation of flexible robots and/or for the design of the control system and for the analysis of its performances. Moreover significant examples, which illustrate the properties of the proposed methodology, are presented; they also show that the proposed modeling methodology is an advisable choice when it is necessary to obtain high precisions, in particular at low frequencies, and/or not prohibitive calculus time, and/or when other modeling methods are inapplicable because of numerical divergence problems.