The performance of a repeatable control scheme for redundant robots

This paper addresses the determination of joint motions for a given end effector displacement in kinematically redundant manipulators. It is well known that velocity control schemes, such as pseudoinverse control, do not guarantee repeatability. But it is possible to obtain repeatable solutions by controlling the manipulator joints so that they behave like elastic couplings. The joint configuration adopted by the manipulator at a given point in task space is one which minimizes the potential energy of the system and is unique. In this paper, we investigate the existence and uniqueness of solutions (joint displacements) for a given end effector displacement. We identify singularities in the algorithm and their physical significance. Finally, we show that it is important to consider the stability of the manipulator at a given configuration and discuss practical considerations in implementing such algorithms