Optimal Trajectories for Vibration Reduction Based on Exponential Filters

Abstract

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

Damped Harmonic Smoother for Trajectory Planning and Vibration Suppression

“…In order to obtain a perfect cancelation even for damped plants, a possible solution consists of translating zeros (and poles) of S 1 (s) along a line parallel to the imaginary axis whose abscissa is equal to the real part of the poles of G ε (s). The procedure used in [20] for rectangular filters, based on a frequency shift of the real quantity σ i and on a modification of the gain in order to assure unitary static gain, has been followed, and the transfer function of the new smoother has been derived:…”

“…where the parameters t 1 , t 2 , p 1 , and p 2 are defined. For more details, see [20]. As for the undamped sinusoidal filter, the choice of the parameters of S σ,i (s) is critical to the level of residual vibration, but in this case, there are two independent variables.…”

“…Similar to the undamped case, the results obtained with the filter S σ,i (s), in terms of PRV, are compared with those produced by a chain of two exponential filters M σ,1 (s)M σ,2 (s), which represent the generalization of the rectangular smoothers M 1 (s)M 2 (s) to consider the damping coefficient of the plant [20] (see Fig. 13).…”

An Online Trajectory Generator on SE(3) for Human–Robot Collaboration

“…Biagiotti et al 13 use a chain of FIR filters to smoothen trajectories to have continuous derivatives of arbitrary order. In [14], the strategy is generalized to produce piecewise exponential jerk profiles, to further reduce machine vibrations. Due to their filtering nature, these approaches again result in time delays and thus neither satisfy R4.…”

An Efficient Algorithm for the Real-Time Generation of Synchronous Reference Signals

“…When discontinuous reference signals are not known in advance, the smoothing action is obtained through real-time methods. To this purpose, several strategies have been proposed in the literature based, for example, on the use of FIR filters [12], [13] or on neuro-fuzzy algorithms [14].…”