Damped Harmonic Smoother for Trajectory Planning and Vibration Suppression

In this brief, a novel filter for online trajectory generation is presented. The filter can be categorized as an input smoother since it acts on the input signal by increasing its continuity level. When fed with simple signals, as, e.g., a step input, it behaves like a trajectory generator that produces harmonic motions. Moreover, it can be combined with other filters, and in particular, with smoothers having a rectangular impulse response, in order to generate (online) more complex trajectories compliant with several kinematic constraints. On the other hand, being a filter, it possesses the capability of shaping the frequency spectrum of the output signal. This possibility can be profitably exploited to suppress residual vibration by imposing that the zeros of the filter cancel the oscillatory dynamics of the plant. For this purpose, the standard harmonic filter has been generalized in order to consider not only the natural frequency but also the damping coefficient of the plant. In this manner, the so-called ``damped harmonic filter" and the related ``damped harmonic trajectory" have been defined. By means of theoretical considerations, supported by experimental tests, the novel approach has been compared with the existing methods, and the advantages of its use have been proved.