Polynomial Piece-Wise Stiffness in Cable-Based Transmissions for Robots: Modeling and Identification

Abstract This paper deals with cable-based motor-to-joint transmissions of multi-link robots chain. Their effects on robots flexibility have to be taken into account for modeling and control design. More in details, slack cables do not provide any force during compression (unlike springs), may present an initial nonzero elongation (preload) and, depending on the material, could exhibit non-constant stiffness. Those features may lead to non-trivial piece-wise elastic torques in a mechanical transmission. In this context, we present a framework to generate a more general (piece-wise) elastic torque model which can be embedded in the classical flexible-joint robot model, coherently with the Lagrangian approach. Moreover, we propose a model based on polynomial stiffness, whose parameters can be identified with ordinary least-squares techniques. Experimental results conducted on a flexible transmission show the usage and the utility of this work.