Multidimensional Trajectories Generation with Vibration Suppression Capabilities: the Role of Exponential B-splines

In this paper, exponential B-spline trajectories are presented and discussed. They are generated by means of a chain of filters characterized by a truncated exponential impulse response. If properly tuned, the filters applied to a vibrating plant are able to cancel the oscillations and in this sense the resulting splines are optimized with respect to the problem of vibrations suppression. Different types of exponential B-spline are illustrated, with one or more exponential filters in the chain, and the procedure for the interpolation of a given set of desired via-points, with a proper choice of the control points, is shown. As a matter of fact, exponential B-splines, generated by means of dynamic filters, combine the vibration suppression capability of input shapers and smoothing filters with the possibility of exactly interpolating some via-points. The advantages of these curves are experimental proved by considering the motion of a spherical pendulum connected to the flange of an industrial robot.