Input Shaping Via B-Spline Filters for 3-D Trajectory Planning

In this paper, the equivalence between uniform B-splines of degree p and the output of a chain composed by p average filters is exploited for optimizing the trajectories used in robotic applications. In particular, the spline trajectories obtained with the proposed generator are characterized from a frequency point of view. Their frequency content is completely determined by the degree p and by the time period T between the equally-spaced knots. It is therefore possible to select these parameters with the purpose of suppressing residual vibrations, that may be present because elastic phenomena affecting the robotic system. In this sense, the proposed approach is very similar to input shaping methods and allows to find a trade-off between two different problems: on one side the requirement of exactly interpolating a set of given points by means of a complex trajectory such as a spline, on the other hand the need of suppressing mechanical vibrations. The effectiveness of the proposed approach is shown by applying it to the generation of a 3D trajectory for a cartesian robot with elastic joints.