Modeling and simulation of flexible manipulators based on a Newton-Euler closed form model

The requirement of increasing performances in manipulators, as well as the trend of mass reduction, motivated by energy efficiency reasons for industrial and aerospace markets, have played a crucial role in robotic and automation control research in the last decade. In this context, modeling of flexible lightweight manipulator structures has been an active topic of research, nevertheless, scientific literature lacks of models for multilink manipulators able to predict the dynamic behavior of flexible robots. In this thesis, a dynamic model of multilink flexible manipulator, described by a set of matrix equations in closed form, is presented. The model is based on the superposition of a nonlinear dynamics for large motion description and linear equations for small elastic displacement. The characterization of flexibility, based on the Floating Frame of Reference (FFR) approach, is achieved by placing an FFR at the base of each link, elastic displacements are described as linear combination of mode shapes, as defined by the Component Modes Synthesis method, based on the Craig-Bempton approach. After development of the mathematical model, a MATLAB/Simulink implementation of the same model is presented, considering for this purpose data of flexible bodies extracted by a frequency analysis followed by a modal reduction performed through FE codes. A set of benchmark problems taken from the literature have been simulated, whereon simulations results have been compared with two commercial multibody software, Modelica/Dymola and MSC Adams, in order to demonstrate the validity of both the mathematical model and the Simulink implementation. Results revealed that both elastic and nonlinear behavior are in good agreement with simulations performed by commercial multibody codes. The Newton-Euler model of the flexible manipulator can now be applied to real world cases, exploiting the computational efficiency of its formulation that allow to design real time controllers, which is the next object of this field of research.