A learning controller for robot manipulators using Fourier series

In this paper, we proposed a new learning controller for decentralized tracking control of nonlinear robot manipulators. When the desired trajectory of each subsystem of the robot lasts for a finite duration, it can be approximated by a Fourier series with constant harmonic magnitudes. Since the elements of the basis of the Fourier space are orthonormal, the tracking control problem in time domain is decentralized into a number of independent regulation problems of the Fourier coefficients, For each subsystem of the robot, a learning controller is designed to individually control each harmonic component of the actual output, although it is cross-related to other components in nonlinear systems. The learning algorithm is designed in a way such that each harmonic magnitude of the actual output converges to that of the desired trajectory within the system bandwidth. Since this decentralized learning controller is designed in Fourier space instead of time domain, the system's time-delay could be easily compensated. This learning controller is only based on the local input and output information; no a priori structure or parameters of the system mode) are required. The control scheme can significantly improve the tracking performance within several trials. The experimental results on 3-DOF direct-drive robot are presented to illustrate the effectiveness of the proposed learning controller.