Bernstein-Be´zier Harmonics and Their Application to Robot Trajectory Synthesis With Minimal Vibrational Excitation

摘要

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-Be´zier form of harmonic trajectory patterns for synthesizing low-harmonic trajectories. Similar to Bernstein-Be´zier polynomial curves, Bernstein-Be´zier harmonic trajectories can be defined either explicitly using Bernstein-Be´zier basis harmonics or recursively using the harmonic deCasteljau algorithm. The second part of the paper demonstrates how a Bernstein-Be´zier trajectory can be combined with the inverse dynamics of a 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.