A parallel algorithm for singular value decomposition as applied to failure tolerant manipulators

Abstract

The system of equations that govern kinematically redundant manipulators is commonly solved by finding the singular value decomposition (SVD) of the corresponding Jacobian matrix. This can require considerable amounts of time to compute, thus a parallel SVD algorithm minimizing execution time is sought. The approach employed here lends itself to parallelization by using Givens rotations and information from previous decompositions. The key contributions of this research include the presentation and implementation of a new variation of a parallel SVD algorithm to compute the SVD for a set of post-fault Jacobians. Results from implementation of the algorithm on a MasPar MP-1 and an IBM SP2 are provided. 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, and the type of parallel architecture used