Input shaping is a method of reducing residual vibrations in computer-controlled machines. Input shaping is implemented by convolving the desired command signal with a sequence of impulses. The result of the convolution is then used to drive the system. Because input shaping alters the commanded trajectory, it has had questionable utility for trajectory following applications such as painting, cutting, and scanning. The effects of input shaping on trajectory following were investigated by simulating the response of a fourth-order system with orthogonal modes and conducting experiments on an XY positioning stage. For nearly all values of experimental parameters, input shaping improved trajectory following.

The authors present an extension to the impulse shaping technique for commanding machines to move with reduced residual vibration. The extension, called frequency sampling, is a method for generating constraints that are used to obtain shaping sequences which minimize residual vibration in systems such as robots whose resonant frequencies change during motion. The authors present a review of impulse shaping methods, a development of the proposed extension, and a comparison of results of tests conducted on a simple model of the Space Shuttle robot arm. Frequency shaping provides a method for minimizing the impulse sequence duration required to give the desired insensitivity.>

A method is described for limiting vibration in flexible systems by shaping the system inputs. Unlike most previous attempts at input shaping, this method does not require an extensive system model or lengthy numerical computation; only knowledge of the system's natural frequency and damping ratio is required. The effectiveness of this method when there are errors in the system model is explored and quantified. An algorithm is presented which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimated natural frequency.>

The authors evaluate a signal generation technique for commanding high-performance machines to move without exciting residual vibration. This time-domain input-shaping technique works like a filter that is designed to eliminate decaying sinusoidal resonance responses. It is compared to a variety of filtering techniques and is shown to perform more effectively than any of them. In particular, frequency-domain filter design techniques are less effective for shaping vibration-reducing inputs to systems. The three-impulse shaping sequence offers significant performance advantages in that moves require less time and result in little or no residual vibration. In addition, the response is not sensitive to variations in the system parameters.>

A method for generating shaped command inputs which reduce endpoint vibration is presented. The technique applies to both open- and closed-loop systems. The Draper Laboratory's Space Shuttle remote manipulator system nonlinear simulator is used to verify the substantial reduction of residual vibration. In addition, the shaped inputs have been designed to closely approximate the time-optimal input, therefore only a small move time penalty is incurred.>