Dynamic modelling of a smart material robot

Three dynamic models of a smart material robot are presented. First, Hamilton´s approach is used to derive an accurate model described by partial differential equations (PDEs), which is not suitable for controller design. Based on the PDEs model, the assumed modes method (AMM) and the finite element method (FEM) are employed to derive two finite dimensional models in the forms of ordinary differential equations which are readily usable for the controller design. All of the models show that a smart material robot cannot be simply treated the same as that of a pure flexible robot. Comparative studies between AMM model and FEM model are carried out in both time and frequency domains to analyze the performance of the system and verify the correctness of the models