PID Stabilization of a Position-Controlled Robot Manipulator Acting Independently of in Collaboration with Human Arm

In this paper we develop framework for PID stabilization of a robot manipulator when using an object independently or in collaboration with a human arm. Inboth applications, the manipulator is equipped with a wrist sensor represented by an impedance. A second order manipulator transfer function along each coordinate direction is assumed. The aim of the paper is to design a PID controller when measurement of contact force, available via wrist sensor, is used to command the positioncontrolled manipulator to a desired position and/or force profile. Necessary and sufficient conditions for stability of the closedloop system are developed using Hermite-Biehler Theorems. The theorems have been used to analyze stability ofpolynomials defined over the set of real numbers. Analgorithm for synthesis ofPID controllers using linear matrixinequalities isdeveloped. The theoretical framework presented in this paper can be easily adapted to other low order manipulator transfer functions.