Impulse Vector: A Basic Mathematical Tool to Design and Analyze Flexible Robots for Removing Residual Vibrations

Flexible robots always accompany residual vibrations during work operations, which should be quickly eliminated to improve productivity. Traditionally, input shapers were designed and analyzed to remove residual vibrations in flexible robots differently for undamped and underdamped systems, and for positive and negative input shapers. This paper presents a unified approach to design and analyze input shapers for undamped and underdamped systems and for positive and negative input shapers using a basic mathematical tool, impulse vector, recently proposed by the first author. The usefulness and effectiveness of the impulse vector method in designing and analyzing input shapers is demonstrated through simulation studies for a second-order system and verified experimentally using a flexible up-and-down device.