An adaptive observer for robots with persistent excitation

Abstract

An adaptive state observer for rigid link manipulators is proposed. The proposed adaptive state observer is based on parametrizing the robot dynamic model via the estimated state and parameters, thus yielding a nominal model plus two perturbation terms, one is linear and the other is quadratic in the state and parameter estimation errors. The update law for the adaptive observer is derived using the MKY lemma (Narendra and Annaswamy 1989). Stability of the origin of the overall error system is shown using the Gronwall-Belmann lemma (Khalil 1992) and a converse Lyapunov theorem (Khalil 1992). The proposed adaptive observer is tested through simulations