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Rodney G. Roberts's PhD Thesis Abstract

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The Design of Repeatable Control Strategies for Kinematically Redundant Manipulators

Ph.D., Purdue University, May 1992

Major Professor: Anthony A. Maciejewski

A kinematically redundant manipulator is a robotic system which possesses more
degrees of freedom than are required to perform its specified task. Due to this
extra freedom, kinematically redundant manipulators offer significant advantages
over traditional non-redundant manipulators, including greater dexterity and the
potential for obstacle and singularity avoidance. However, under certain control
strategies, a kinematically redundant manipulator may not be repeatable when
performing a cyclic task. A control strategy is said to be repeatable if the
manipulator returns to its initial configuration when the end effector traces a
closed path in the workspace. This is a particularly important property for a
manipulator to have when performing a cyclic task since the manipulator's
behavior would otherwise be difficult to predict without prior analysis.

Unfortunately, many optimal control strategies are not repeatable in the above
sense. This work presents two methods for choosing repeatable inverses which
are "close" to a given desired nonrepeatable inverse, with the pseudoinverse
serving as an illustrative example. The first approach is to minimize the
distance of a repeatable inverse from the desired nonrepeatable inverse in an
integral norm sense. This is done by minimizing the integral of the square of
the matrix norm of the difference of the two inverses over a select region of
the joint space. The second approach is to minimize the difference of the
associated null spaces of the two inverses, which results in a computationally
easier optimization than the first approach.