@article{ONeil98,
title = {On the existence and characteristics of solution paths at algorithmic
singularities},
author = {K. A. O'Neil and Y. C. Chen and J. Q. Seng},
journal = {IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION},
month = {April},
number = {2},
pages = {336-342},
volume = {14},
year = {1998},
description = {robotica-bib},
abstract = {The extended Jacobian method is a popular approach for controlling
a kinematically redundant arm which allows one to resolve redundancy
by locally optimizing an objective function and to gain repeatability
for a cyclic end effector trajectory, It is a special case of a family
of methods called constraint function methods. It has been found
that the occurrence of algorithmic singularities ran clause severe
difficulties and the advantages of the methods such as repeatability
might no longer exist. The purpose of this paper is to study the
characteristics of algorithmic singularities, especially those of
corank 1. A result of the authors on kinematic singularities is used
to obtain a sufficient condition for the existence of solution paths
at algorithmic singularities of the constrained function method.
The phenomenon of branch repeatability is shown to occur at an algorithmic
singularity. We also show that the extended Jacobian method cannot
successfully optimize the objective function beyond the singularity
without loss of continuity of the joint derivative. Examples are
given to demonstrate the use of our theoretical results.},
keywords = {imported }
}
::