Robust adaptive controller design and stability analysis for 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 adaptive control scheme is developed with special attention to stability and robustness of the controller. The proposed controller is based on online identification of the manipulator parameters and 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, an example of a two-link flexible-joint manipulator is considered. Simulation results are given to illustrate the applicability of the proposed control scheme