Since all robots have some inherent flexibility, fast motions tend to excite system vibrations. This paper develops shaped inputs that generate fast motions with minimum residual vibration. Shaped force inputs are constructed from a versine series, with coefficients of the harmonic terms chosen to maximize kinetic energy and minimize excitation energy at the system natural frequencies. These force inputs are doubly integrated to obtain position waveforms that serve as reference profiles for a closed-loop controller. A Cartesian robot is used as an experimental system to test these shaped reference inputs and to compare their responses to simple step responses. Results indicate considerable reduction in residual vibration with the shaped inputs. This is especially useful when modal coupling exists, since vibration in other axes can be prevented by driving the moving axis with shaped inputs having no excitation energy at the coupled mode frequencies.

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