A Regressor-free Adaptive Control for Flexible-joint Robots based on Function Approximation Technique

An adaptive controller is presented in this paper to control an n-link flexible-joint manipulator with time-varying uncertainties. The function approximation technique (FAT) is utilized to represent time-varying uncertainties in some finite combinations of orthogonal basis. The tedious computation of the regressor matrix needed in traditional adaptive control is avoided in the new design, and the controller does not require the variation bounds of time-varying uncertainties needed in traditional robust control. In addition, the joint acceleration is not needed in the controller realization. Via the Lyapunov-like stability theory, adaptive update laws are derived to give convergence of the output tracking error. Moreover, the upper bounds of tracking errors in the transient state are also derived. A 2 DOF planar manipulator with flexible joints is used in the computer simulation to verify the effectiveness of the proposed controller.