BERNSTEIN-BEZIER HARMONICS AND THEIR APPLICATION TO ROBOT TRAJECTORY SYNTHESIS WITH MINIMAL VIBRATIONAL-EXCITATION

For a given high-speed machinery, a significant source of the internal ly induced vibrational excitation is the presence of high frequency ha rmonics in the trajectories that the system is forced to follow. This paper presents a Bernstein-Bezier form of harmonic trajectory patterns for synthesizing low-harmonic trajectories. Similar to Bernstein-Bezi er polynomial curves, Bernstein-Bezier harmonic trajectories can be de fined either explicitly using Bernstein-Bezier basis harmonics or recu rsively using the harmonic deCasteljau algorithm. The second part of t he paper demonstrates how a Bernstein-Bezier trajectory can be combine d with the inverse dynamics of a robot manipulator for synthesizing a joint trajectory that demands ''minimal'' dynamic response from its ac tuators. An example involving a planar 2R robot is also presented.