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

[+] Author and Article Information
Q. J. Ge, J. Rastegar

Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brock, NY 11794-2300

J. Mech. Des 118(4), 509-514 (Dec 01, 1996) (6 pages) doi:10.1115/1.2826920 History: Received December 01, 1995; Revised June 01, 1996; Online December 11, 2007


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

Copyright © 1996 by The American Society of Mechanical Engineers
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