A Regressor Free Adaptive Backstepping Design of Flexible Joint Robot Based on Function Approximation Technique

In this paper a function approximation technique is proposed for adaptive back stepping design of a flexible¡Vjoint robot manipulator. The dynamics of the robot manipulator are derived with the assumption that all matrices in this robot model are unknown. Since these matrices are time varying and their variation bounds are not given, traditional adaptive or robust control schemes cannot be applied. The function approximation technique is employed here to represent uncertainties in some finite linear combinations of the orthogonal basis. Using the Lyapunov stability theory, a set of update law is derived to give closed loop stability with proper tracking performance. A two-link flexible-joint robot is used in the computer simulation to verify validity and effectiveness of the proposed control law.