Tracy D. Braun's MSEE Thesis Abstract

Parallel Algorithms for Singular Value Decomposition as Applied to Failure Tolerant Manipulators

MSEE, Purdue University, Dec. 1997

Co-Major Professors: H. J. Siegel and Anthony A. Maciejewski

Kinematically redundant robotic manipulators have a greater number of independently controlled joints than are necessary to achieve the desired motion. Thus, kinematically redundant manipulators offer additional degrees of freedom that can be used to provide fault tolerance. The system of equations that govern kinematically redundant manipulators are frequently solved by finding the singular value decomposition (SVD) of the corresponding Jacobian matrix. This system of equations, however, can require considerable amounts of time to solve, especially when the complete SVD is required.

To minimize the time required to compute the SVD, a parallel algorithm is sought. The approach used here lends itself to parallelization by using Givens rotations and information from previous decompositions. This reduces the number of iterations necessary to decompose the current Jacobian matrix. Fault tolerance information for the manipulator can be provided if the SVD for a set of Jacobians, each representing a single locked-joint failure for the manipulator, is also determined. The key contributions of this research include the presentation and implementation of two new variations of a parallel SVD algorithm to compute the SVD for a set of post-fault Jacobians. All implementations are performed on an SIMD MasPar MP-1. The implementations can be used to facilitate real-time control, fault tolerance analysis, and faster simulation. Specific issues considered for each implementation include data mapping, the effect that increasing the number of processors has on execution time, and the type of parallel architecture used. These implementations show that an application must be adapted to a particular target platform to exploit that architecture's features, The resulting timing information and error analysis shows that these are viable real-time control and simulation schemes.