Optimal Trajectories for Vibration Reduction Based on Exponential Filters

In this paper, a new type of trajectory, based on an exponential jerk, is presented along with filters for their online generation. The goal is to generalize constant jerk trajectories, widely used in industrial applications, in order to reduce vibrations of motion systems. As a matter of fact, constant jerk trajectories do not assure a complete vibration suppression when the damping of the resonant modes is not negligible. The values of the parameters (decay rate and duration) of the jerk impulses that allow residual vibration cancellation are derived in an analytical way as a function of the dynamic characteristics of the plant. Comparisons with the well-known input shaping techniques and with system-inversion-based filters show the advantages of the proposed method in terms of robustness with respect to modeling errors, smoothness of the resulting trajectory, and time duration of the motion under velocity and acceleration constraints.