Non-identical Trajectories Tracking Of Flexible Manipulator Using Function Approximation Based Iterative Learning

The flexible manipulator is nonminimum phase, high non-linearity, high-coupling uncertain system, so the tip tracking is very difficult. Together with the computation consumption and equipment costs, these are disadvantages which hinder the robotic manipulators from doing jobs requiring higher accuracy and speed.In this paper, we propose a new iterative learning control scheme for trajectory tracking of the flexible manipulator, which can let the manipulators follow the expected trajectory by iterative learning without accurate model. In real robotic systems, there are many constraints, such as the expected trajectory changes, which are not in accordance with the assumption of iterative learning algorithm and bring difficulties to its application. Thus, to design an iterative learning algorithm to adjust the trajectory changes and exact tip tracking is one of my works in this paper.This paper is organized as follows:1 Considering the affine nonlinear dynamic system, we propose a new iterative learning control scheme with variable structure technique. And the convergence is proven by applying Lyapunov-like composite energy function.2 Then we design the controllers with three common function approximation methods and the simulation results demonstrate our algorithm can exactly follow the non-identical trajectories. Through the comparison of these methods, we find out the wavelet network is the better one.3 Then we simulate the flexible manipulator with our iterative learning controller based on wavelet network approximation, the result shows that the flexible manipulator can not only exactly follow the non-identical trajectories, but also the vibration elimination is perfect.4 According to the hardware equipment in our laboratory, we design the control system of the flexible manipulator. We also construct the model with SimMechanics toolbox in MATLAB. The convergence of the tracking error is shown by a simulation on this model, the vibration is also eliminated. That demonstrates the effects of the algorithm.