Adaptive Boundary Control of Flexible Manipulators with Parameter Uncertainty Based on RBF Neural Network

Cang He,Jinhui Jiang,Fang Zhang,Fabio Rizzo

doi:10.1155/2020/8261423

Abstract

In this paper, nonlinear dynamical equations of the flexible manipulator with a lumped payload at the free end are derived from Hamilton's principle. The obtained model consists of both distributed parameters and lumped parameters, namely, partial differential equations (PDEs) governing the flexible motion of links and boundary conditions in the form of ordinary differential equations (ODEs). Considering the great nonlinear approximation ability of the radial basis function (RBF) neural network, we propose a combined control algorithm that includes two parts: one is a boundary controller to track the desired joint positions and suppress the vibration of flexible links; another is a RBF neural network designed to compensate for the parametric uncertainties. The iteration criterion of the RBF neural network weight matrix is derived from the extended Lyapunov function. Stabilization analysis is further carried out theoretically via LaSalle’s invariance principle. Finally, the results of the numerical simulation verify that the proposed control law can realize the asymptotic convergence of tracking error and suppression of the elastic vibration as well.

Highlights

Flexible manipulators are widely used in automation field including space station solar array and advanced robots, as well as mechanical manufacture
In spite of the convenience, some defects still exist in these methods, such as spillover instability caused by neglected higher modes, error of mode truncations, and higher order of the controller
It means that no offline training or learning process is needed for the designed RBF neural network (NN) and the approximation could be completed during the operation of the flexible manipulator

Summary

Introduction

Flexible manipulators are widely used in automation field including space station solar array and advanced robots, as well as mechanical manufacture. Liu et al established a boundary control algorithm for a flexible double-link manipulator based on the PDE dynamic model [6]. Rogers et al applied RBF NN to generate an orthogonal basis to estimate the uncertain parameters [23] He et al proposed one RBF NN to approximate the estimated input dead-zone effect, and another RBF NN is used to estimate the unknown dynamics of the flexible manipulator [24]. In comparison with previous work, we note that the outlined novelty of this paper (1) Utilizes a more complete dynamic model containing multiuncertain parameters and build the co-influence function of the uncertainty (2) Combines the boundary control with RBF NN to deal with different parameter uncertainties.

Dynamic Model

Adaptive Boundary Control Strategy

Stability Analysis

Numerical Simulation

Conclusions