Qj. Ge et J. Rastegar, BERNSTEIN-BEZIER HARMONICS AND THEIR APPLICATION TO ROBOT TRAJECTORY SYNTHESIS WITH MINIMAL VIBRATIONAL-EXCITATION, Journal of mechnical design, 118(4), 1996, pp. 509-514
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.