Residual vibration suppression in uncertain systems: A robust structural modification approach to trajectory planning

In this paper a novel method to improve the residual vibration suppression in underactuated uncertain flexible systems through motion planning is proposed. The proposed technique relies on the concurrent use of input shaping and on the alteration of the mechanical properties of the system, which enables the enhancement of the robustness to uncertain parameters. Robustness is formulated through the parametric sensitivities of the natural frequencies that provide an analytical and non-probabilistic tool, which is embedded in the eigenstructure assignment algorithm developed in this work. The effectiveness of the proposed method is assessed through a benchmark testbed composed by a triple pendulum attached to a delta robot, that should execute rest-to-rest, residual vibration-free motion. Hence, residual vibrations of the pendulum are used to measure the accuracy and the sensitivity of the proposed combined shaper-IDSM approach. Both the numerical and experimental results confirm the advantages of the proposed technique for the suppression of the residual vibrations in uncertain systems over traditional techniques. In particular, robustness of the dominant tuning frequency is increased with respect to variations of the tip-end mass of the pendulum, representing a varying payload transferred by a robotic system