Control of Robotic Systems with Flexible Components Using Hermite Polynomial-Based Neural Networks

Abstract

Flexible-link robots comprise an important class of systems that include lightweight arms for assembly, civil infrastructure, bridge/vehicle systems, military applications and largescale space structures. Modelling and vibration control of flexible systems have received a great deal of attention in recent years (Kanoh, Tzafestas, et. al., 1986), (Rigatos, 2009), (Rigatos, 2006), (Aoustin, Fliess, et al.,1997 ). Conventional approaches to design a control system for a flexible-link robot often involve the development of a mathematical model describing the robot dynamics, and the application of analytical techniques to this model to derive an appropriate control law (Cetinkunt & Yu, 1991), (De Luca & Siciliano, 1993), (Arteaga & Siciliano, 2000). Usually, such a mathematical model consists of nonlinear partial differential equations, most of which are obtained using some approximation or simplification (Kanoh, Tzafestas, et al., 1986), (Rigatos, 2009). The inverse dynamics modelbased control for flexible link robots is based on modal analysis, i.e. on the assumption that the deformation of the flexible link can be written as a finite series expansion containing the elementary vibration modes (Wang & Gao, 2004). However, this inverse-dynamics modelbased control may result into unsatisfactory performance when an accurate model is unavailable, due to parameters uncertainty or truncation of high order vibration modes (Lewis, Jagannathan & Yesildirek, 1999). In parallel to model-based control for flexible-link robots, model-free control methods have been studied (Rigatos, 2009), (Benosman & LeVey 2004). A number of research papers employ model-free approaches for the control of flexible-link robots based on fuzzy logic and neural networks. In (Tian & Collins, 2005) control of a flexible manipulator with the use of a neuro-fuzzy method is described, where the weighting factor of the fuzzy logic controller is adjusted by a dynamic recurrent identification network. The controller works without any prior knowledge about the manipulator's dynamics. Control of the endeffector's position of a flexible-link manipulator with the use of neural and fuzzy controllers has been presented in (Wai & Lee, 2004), (Subudhi & Morris, 2009), (Talebi, Khorasani, et. al, 1998), (Lin & Lewis, 2002), (Guterrez, Lewis & Lowe, 1998). In (Wai & Lee, 2004) an 25