On the modeling and identification of stiffness in cable-based mechanical transmissions for robot manipulators

Abstract In this paper, we consider cable-based motor-to-joint transmissions which are known to introduce flexibility phenomena in the dynamic behaviour of robot manipulators. Their effects 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 conventional identification techniques. The goal is to provide a precise characterization of the elastic torques in a cable-based transmission in order to support mechanical design, preload tuning and finally, to quantify the eventual error introduced by relying on simpler models such as the linear one. The targeted scope is about multi-link cable-driven robots chain (as it may be the case for compact or lightweight robots for instance, finger hand being viewed generally as a serial small-scaled robot arm). Some theoretical examples related to the multi-joint case, as well as experimental results conducted on a 1-dof flexible transmission, show the usage and the utility of this work.