A nonlinear finite element formalism for modelling flexible and soft manipulators

This paper presents a nonlinear finite element formalism for modelling the dynamics of flexible manipulators using the special Euclidean group SE(3) framework. The method is based on a local description of the motion variables, and results in a singularity — free formulation which exhibits important advantages regarding numerical implementation. The motivation behind this work is the development of a new class of model — based control systems which may predict and thus avoid the deformations of a real flexible mechanism. Finite element methods based on the geometrically exact beam theory have been proven to be the most accurate to account for flexibility: in this paper we highlight the key aspects of this formulation deriving the equations of motion of a flexible constrained manipulator and we illustrate its potential in robotics through a simple case study, the dynamic analysis of a two-link manipulator, simulating different model assumptions in order to emphasize its real physical behavior as flexible mechanism.

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