The currently accepted method to create smooth position profiles is to fit polynomial blends or other functions between linear regions of constant velocity. The coefficients of the blended regions are usually computed by matching derivatives, or any other required parameter, at the end points. The conventional use of polynomial blends for motion profiling has several limitations. The two most restrictive limitations are the requirement to pre-compute, and the limited smoothness of the profiles. The coefficients of each blending segment must be pre-computed before a segment can be traversed and, in many situations, the smoothing of the entire profile is required before motion can start. The degree of the blending segments is usually limited to third order polynomials to control unwanted inflections in the resulting curve. Higher order polynomials can be used if both the adjoining segments have a zero slope. But with higher order polynomials comes the issue of computing the polynomial coefficients. Past third order, generic closed form solutions for the polynomial coefficient do not exist, requiring a set of five or more linear equations be solved for each blend.
This dissertation significantly advances the area of motion profiling by introducing and expanding four areas of time-position profiling. FIR profiling is expanded by characterizing the effect of Boxcar filter duration and the introduction of an infinitely continuous kernel. The area of break-point profiling is introduced by demonstrating a new method to create closed form high order even-ordered polynomial profiles. Break-point profiling is further advanced by creating closed-form Gaussian-based profiles. The area of vibration-free motion is advanced by showing how to use the components of the original twin pulse profile to significantly reduce residual vibrations. Vibration-free motion is further enhanced by showing how to use the underlying base profile of input-shaping to create wide-band suppression of induced vibrations. And finally a new form of profiling is introduced that consumes constant power as the profile is traversed.
|Advisor:||Starr, Gregory P.|
|School:||The University of New Mexico|
|School Location:||United States -- New Mexico|
|Source:||DAI-B 70/02, Dissertation Abstracts International|
|Subjects:||Mechanical engineering, Robotics|
|Keywords:||Input shaping, Motion profiling, Vibration suppression|
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