Near-pseudoinverse control of kinematically redundant manipulators with the constraint of repeatability

The issue of repeatability for a particular redundant manipulator is considered. The manipulator considered is a planar three-link manipulator with two orthogonal, prismatic joints and a third revolute joint. It can be thought of as a mobile robot with one revolute joint. It is shown that pseudoinverse control has no stable surfaces for this robotic manipulator. A class of repeatable inverses is then derived. The repeatable inverse which is closest in an integral norm sense to the pseudoinverse is found from this class.<>