PID stabilization of a position controlled manipulator with wrist sensor

In this paper we discuss PID stabilization of a position-controlled manipulator equipped with a wrist sensor using the Hermite-Biehler theorem framework. A second order transfer function for the manipulator is assumed along each coordinate direction that can be replaced by unity gain at slow speeds of manipulation. The wrist sensor impedance is similarly represented by a second order transfer function. The Hermite-Biehler theorem is used for the stability analysis of the closed-loop system. The general theoretical framework presented here can be easily adapted to other low order plant models.