Experimental study of nonlinear normal modes in robotics: analysis and control strategies

Abstract

Robots are used in a wide variety of tasks ranging from search and rescue, manufacturing and palletizing applications. In the last twenty years there has not only been interests in accurate robots but also compliantly actuated robots which resembles more the human dynamical capabilities. Research has shown that physical compliance is key to increase a robot’s mechanical robustness and explosiveness, which allows to outperform the dynamics of stiff robots. Besides that, the energy storing capabilities promises more energy efficient cyclic motions. However, there exist still no general method to generate energy efficient motions for complex scenarios such as manipulation. Normal modes are specific patterns of motion or vibration that a system can exhibit, and they are important for understanding the underlying dynamics of a system. Executing motions close to the normal modes of the system can potentially results in more efficient cyclic motions. While linear normal modes (LNMs) exactly characterize linear systems, this is not the case for nonlinear dynamical systems where a different framework is necessary to obtain nonlinear normal modes (NNMs). It is still unknown whether NNMs can be used to perform cyclic movements in a more energy efficient way on a real-life compliantly actuated system. Another research question is, what are the effects of various parameters on these NNMs such as change in stiffness settings and change in energy due to damping and friction. These questions will be investigated in this work. First, NNMs will be identified and analysed which are interesting for particular hammering motions on the 4 DOF left arm system of the anthropomorphic compliantly actuated robot David using a nonlinear normal modes toolbox developed at the German Aerospace Center (DLR). Further, a new control strategy is developed named Energy Pumping (EP) Control to stabilize the modes by compensating for energy losses due to frictions or to switch to modes on different energy levels. Finally, this control algorithm is compared to Elastic Structure Preserving (ESP) Control in terms of performance and the effect of intentional impacts on the modes has been analysed.