COMMAND SHAPING

Input Shaping is a subset of the larger field of Command Shaping, or feedforward control. Input shaping usually refers to the process of generating shaped commands by convolution with an impulse sequence, or by a process which can be interpreted as convolution with an impulse sequence. However, shaped commands can be generated by other methods. For instance, smooth command profiles can be generated by superposition of trigonometric functions. The resulting commands can decrease the system vibration.

Here is a very brief sampling of command shaping papers:
Aspinwall, D. M., Acceleration Profiles for Minimizing Residual Response, 1980, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 102(March), pp. 3-6.
Farrenkopf, R. L., Optimal Open-Loop maneuver Profiles for Flexible Spacecraft, 1979, Journal of Guidance and Control, Vol. 2(6), pp. 491-498.
Junkins, J. L., Rahman, Z. H. and Bang, H., Near-Minimum Time Control of Distributed Parameter Systems: Analytical and Experimental Results, 1991, Journal of Guidance, Control, and Dynamics, , pp. 406-415.
Meckl, P. H. and Kinceler, R., Trajectory Determination for Vibration-Free Motions of a Flexible-joint Robot, 1994, Proceedings of the American Control Conference, Baltimore, MD, Vol. 3, pp. 2521-2525.
Meckl, P. H. and Seering, W. P., Minimizing Residual Vibration for Point-to-Point Motion, 1985, Journal of Vibration, Acoustics, Stress and Reliability in Design, Vol. 107(October), pp. 378-382.
Schiller, Z. and Chang, H., Trajectory Preshaping for High-Speed Articulated Systems, 1993, submitted to the ASME Journal of Dynamic Systems, Measurement, and Control, .
Singer, N. C. and Seering, W. P., Using Acausal Shaping Techniques to Reduce Robot Vibration, 1988, Proceedings of the IEEE International Conference on Robotics and Automation, Philadelphia, PA, Vol. 3, pp. 1434-1439.
Swigert, C. J., Shaped Torque Techniques, 1980, Journal of Guidance and Control, Vol. 3(5), pp. 460-467.
Wiederrich, J. L. and Roth, B., Design of Low Vibration Cam Profiles, 1974, Conference on Cams and Cam Mechanisms, Liverpool, England, Vol. 1.
Wiederrich, J. L. and Roth, B., Dynamic Synthesis of Cams Using Finite Trigonometric Series, 1975, ASME Journal of Engineering for Industry, Vol. ???(February), pp. 287-293.