Stability problems of robotic systems arise sometimes suddenly, seemingly for no reason. The digital time sampling is often the main cause of these instabilities. Discrete models, which are capable of the prediction of stability, are available for low-degree-of-freedom template models of linear position and force control. However, for the inverse dynamics control of underactuated systems, the literature has a lack of generally applicable results related to the effect of time discretization. Several control approaches are available in the literature out of which a widely used one, the augmented Lagrangian formalism and its stability properties are analysed in this work. Theoretical stability properties are obtained for a generally usable, linear, underactuated, two-degree-of-freedom constrained template model. The actuator dynamics, the finite difference approximation of the feedback velocity and the filtering of the feedback data are considered in the model. These phenomena strongly affects the stability properties. The theoretically obtained stability maps are experimentally validated on an underactuated crane-like indoor robot. The position and orientation accuracy of the robot were assessed: the absolute position error was below 30 mm and the orientation error was below 3°.

The energy dissipation in assembled metal structures is mainly related to various physical phenomena – usually modelled as dry friction – on the contact surfaces. However, the reliable numerical modelling of assemblies is a challenging task due to the complexity of the contact mechanisms. To fit the models to experimental results, it is beneficial if the material damping can be separated from the contact damping. The paper presents measurement results aiming to distinguish material damping from the damping related to the contact between the conforming surfaces of assembled machine parts. To evaluate the role of contact in damping and to find a connection between the contact-related increase of modal damping and the mode shapes, the modal damping ratios of a monolithic body and a shrink-fitted assembly are compared. It is demonstrated that the contact damping is linear in the examined case. Based on the experiments, a finite element (FE) model was developed that does not apply computationally expensive contact algorithms. The FE model was able to reproduce the measured modal damping values of the assembled structure at all the natural frequencies that fell in the frequency range of the measurement. This result is achieved by fitting only a single damping parameter. The research work is motivated by metal cutting, where the damping of the machine-tool-workpiece loop plays a key role in the stability of the process, particularly in case of high speed machining.