Dynamic Modelling of Flexible Manipulator based on a Large Number of Finite Elements

Abstract

This paper focuses on the issue of tracking the trajectory of a flexible arm. The purpose is to ensure the flexible arm follows the desired path in the joint space. To achieve our objective, we have three problems to solve: modeling, control, and trajectory planning. As in the case of rigid robots, the Euler-Lagrange formulation remains valid with the exception of dividing the flexible arm into a finite number of elements to model the deformation. The iterative learning control scheme can be used to achieve perfect tracking throughout the movement period, a sufficient condition based on the bounded real lemma that guarantees the convergence error between iteration is given. All the results are presented in terms of linear matrix inequalities synthesis (LMIs).