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Tracy D. Braun's MSEE Thesis Abstract

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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.