Flexible Links Manipulators: from Modelling to Control

Abstract

This paper relates recent results obtained in the field of modelling and control of flexible link manipulators and proposes an investigation of the problem raised by this type of systems (at least in the planar case). First, adopting the modal floating frame approach and the Newton–Euler formalism, we propose an extension of the models for control to the case of fast dynamics and finite deformations. This dynamic model is based on a nonlinear generalisation of the standard Euler–Bernoulli kinematics. Then, based on the models recalled we treat the end-effector tracking problem for the one-link case as well as for the planar multi-link case. For the one-link system, we propose two methods, the first one is based on causal stable inversion of linear non-minimum phase model via output trajectory planning. The other one is an algebraic scheme, based on the parametrization of linear differential operators. For the planar multi-link case the control law proposed is based on causal stable inversion over a bounded time domain of nonlinear non-minimum phase systems. Numerical tests are presented together with experimental results, displaying the well behaved of these approaches.