Bernstein-Bézier Harmonics and Their Application to Robot Trajectory Synthesis With Minimal Vibrational Excitation

For a given high-speed machinery, a significant source of the internally induced vibrational excitation is the presence of high frequency harmonics 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-Bezier polynomial curves, Bernstein-Bezier harmonic trajectories can be defined either explicitly using Bernstein-Bezier basis harmonics or recursively using the harmonic deCasteljau algorithm. The second part of the paper demonstrates how a Bernstein-Bezier trajectory can be combined with the inverse dynamics ofa robot manipulator for synthesizing a joint trajectory that demands minimal dynamic response from its actuators. An example involving a planar 2R robot is also presented.