Stability of Linear Feedback Control

Abstract

Abstract A set of linear PD (proportional and differential) servo-loops installed independently and locally at each joint actuator establishes global asymptotic stability for set point position control, provided that the gravity force is compensated carefully. Without compensation for the gravity term, linear and distributed PIO servo-loops establish an asymptotic stability in a local sense. These control schemes can be extensively applied to robot dynamics with flexible joints, under holonomic tool endpoint constraint, or under coordination control of multiple arms. In order to make the argument simple, we consider a class of anthropoid robot manipulators with all revolute-type joints (see Fig. 2.1).