Adaptive learning control of uncertain robotic systems

Abstract

An adaptive learning control scheme is presented for uncertain robotic systems that is capable of tracking the entire profile of the reference input. The control scheme consists of three control blocks: a linear feedback, a feedforward error compensation and a learning strategy. At each iteration, the linear feedback with the feedforward error compensation provides stability of the system and keeps its state errors within uniform bounds. The learning strategy, on the other hand, estimates the desired control input and uncertain system parameters, which are used to track the entire span of a reference input over a sequence of iterations. In contrast with many other learning control techniques, the proposed learning algorithm neither uses derivative terms of feedback errors nor assumes any perturbations on the learning control input as a prerequisite. The parameter estimator neither uses any joint acceleration terms nor uses any inversion of the estimated inertia matrix, which makes its implementation practical. The proposed controller is superior to the high-gain feedback based learning controller (Kuc et al. 1991) because the magnitude of linear feedback gains required to guarantee convergence of the learning controller can be made much smaller thereby solving the problems of actuator saturation or actuator overdesign. The convergence proof of the learning scheme with or without parameter estimation is given under mild conditions on the feedback gains and learning control gains. Under the condition of persistent excitation in the domain of iteration sequence, it is proved that the estimated system parameters also converge to the true parameters.