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.