Tracking of discrete-time unmodeled reference signals in robotic manipulators using output regulation theory and high-gain observers

In the field of control, output regulation theory ensures the tracking of reference signals generated by a known dynamic exogenous system, referred to as the exosystem. However, there are applications where the exosystem may be unknown. In this context, the present paper proposes a controller based on Francis output regulation theory, where a high-gain observer (HGO) is used to estimate the states of the unmodeled reference signals. This observer is structurally integrated into the discrete form of Francis output regulation equations as the exosystem. The proposed approach assumes that discrete-time unmodeled reference signals are obtained by transforming a given trajectory from the workspace into joint space of a robotic manipulator. Consequently, the accuracy of motion in Cartesian space depends on the tracking error in each joint. As a case study, a two-degree-of-freedom robot is presented, and its dynamic model is used as the basis for constructing the controller. Finally, simulations are performed using a multibody model developed in Simulink-Simscape to demonstrate that the proposed controller satisfies the stability and asymptotic regulation criteria.