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

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 EulerLagrange 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). Keywords—Single-link flexible arm; finite element; trajectory tracking; iterative learning control; linear matrix inequality; bounded real lemma