Observer-based robust task-space control of robot manipulators using Legendre polynomial

In this paper, a simple observer-based robust control of robot manipulators in the task-space is presented. Many nonlinear observers require system dynamics. The novelty of this paper is designing a simple model-free observer for robot manipulators using orthogonal functions theorem. Based on this theorem, orthogonal functions such as Legendre polynomials are universal approximators. The controller is consisted of a state feedback gain using the observed states and an uncertainty estimator using Legendre polynomials. Using Lyapunov stability theorem, it is guaranteed that the controller tracking error and also the observer estimation error converge to zero. The case study is a SCARA robot manipulator driven by permanent magnet DC motors. Simulation results verify the effectiveness of the proposed algorithm.