Parallel approaches for singular value decomposition as applied to robotic manipulator Jacobians

Authors:
Tracy D. Braun;Renard Ulrey;Anthony A. Maciejewski;Howard Jay Siegel
Affiliations:
NOEMIX, 1425 Russ Blvd. Ste. T-110, San Diego, California;AMCC Corporation, 4715 Innovation Dr., Fort Collins, Colorado;Electrical and Computer Engineering Department, Colorado State University, Fort Collins, Colorado;Electrical and Computer Engineering Department and Computer Science Department, Colorado State University, Fort Collins, Colorado
Venue:
International Journal of Parallel Programming
Year:
2002

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Abstract

The system of equations that govern kinematically redundant robotic manipulators is commonly solved by finding the singular value decomposition (SVD) of the corresponding Jacobian matrix. This can require a considerable amount of time to compute, thus a parallel SVD algorithm reducing execution time is sought. The approach employed here lends itself to parallelization by using Givens rotations and information from previous decompositions. The key contribution of this research is the presentation and implementation of parallel SVD algorithms to compute the SVD for a set of Jacobians that represent various different joint failure scenarios. Results from implementation of the algorithm on a MasPar MP-1, an IBM SP2, and the PASM prototype parallel computers are compared. Specific issues considered for each implementation include: how data is mapped to the processing elements, the effect that increasing the number of processing elements has on execution time, the type of parallel architecture used, and trade-offs between modes of parallelism.