Trajectory following robust adaptive control of flexible joint manipulators

The problem of controlling robot manipulators with flexible joints is considered. A reduced-order flexible joint model based on a singular perturbation formulation of the manipulator equations of motion is used. The concept of an integral manifold is utilized to construct the dynamics of the slow subsystem. A fast subsystem is constructed to represent the dynamics of the elastic forces at the joints. A composite control scheme is developed based on online identification of the manipulator parameters which takes into account the effect of a class of unmodeled dynamics, identification errors and parameter variations. Stability analysis of the resulting closed-loop full-order system is presented. To show the capability of the proposed algorithm, a numerical examples is included for a two-link flexible-joints manipulator