Optimization of Generalized S-Curve Trajectories for Residual Vibration Suppression and Compliance With Kinematic Bounds

This article proposes a new optimization algorithm that assures the minimum possible duration of generalized S-curve trajectories compliant with kinematic limitations and capable of suppressing residual vibrations when tracked by a resonant plant. Thanks to the possibility of generating such kind of trajectories with a chain of filters, called smoothers, each one characterized by a single parameter, i.e., the duration
$T_i$
of its impulse response, the optimization process aims at minimizing the order of the trajectory, and accordingly the number of smoothers in the chain, and leads to rest-to-rest trajectories that, under the given specifications, cannot be made shorter in time. Therefore, the structure of the trajectory is not predetermined but is the outcome of the proposed algorithm together with the optimal parameters defining it. The effectiveness of the proposed approach is proven by applying the designed trajectories to an experimental setup based on a flexible link.