Single-mode input shaping for multi-mode vibration suppression in flexible robotic manipulators: an experimental validation of mode alignment via mass addition

Controlling multi-mode vibrations in flexible manipulators is challenging, particularly in nonlinear systems. This paper introduces and experimentally validates an approach for multi-mode vibration suppression via single-mode input shaping, achieved by aligning the second vibration mode to an odd multiple of the first through strategic mass addition. This technique simplifies control design and reduces computational complexity by employing an open-loop command that only targets the first vibration mode. Furthermore, it is found that conventional linear models fail to predict the nonlinear dynamics induced by mass addition, motivating the development and validation of a high-fidelity numerical model. The experimental findings demonstrate that single-mode shaping can effectively suppress multi-mode vibrations in nonlinear flexible systems, offering a practical and efficient solution for flexible robotic manipulators.