Adaptive Lqr-based Control of 3 Dof Spherical Articulated Robotic Manipulator

Abstract

Abstract In this work, an Adaptive Linear Quadratic Regulator (LQR) is proposed for the tracking control of a 3 DOF articulated robotic manipulator. The main objective of this work is to drive the robotic manipulator to its equilibrium point from any initial position of the end effector of a robotic manipulator in an adaptive way even if the system dynamics consist of modelling uncertainties. The conventional LQR is able to provide a good measure of robustness against disturbances and achieve good tracking performance. However, it will give degraded tracking performance in case of the presence of model uncertainties. Therefore LQR tracking performance is enhanced by using a Model Reference Adaptive Controller (MRAC) in the literature for enabling a 2 DOF system to achieve good tracking against modelling uncertainties. But it has not been applied for a 3 DOF system till date. Therefore in this work, it is proposed to be applied for such a system for the first time to realize an adaptive control. The forward and inverse kinematics level equations are formulated using an indirect form of the Denavit Hartenberg (DH) convention. The dynamics of robotic manipulator are derived using the Euler-Lagrange formulation. The dynamics of manipulator with the LQR control are considered to be the reference dynamics for the MRAC control and the modelling uncertainty will be added to the system dynamics to test its performance. The MRAC augmented LQR provides faster convergence with improved stability against modelling uncertainties.