A new approach of vibrations control in robotics

We present here in the framework of resonant behaviors an eigenfrequency invariance property for loaded flexural and torsional deformable bodies very suitable for the design of finite and precise controllers in the problem of vibrations control in robotics. We found that under a preload condition each eigenfrequency is invariant versus the tipload m_N. For the mode 7 and beyond the preload conditions are less than m_N = 1, and the seven first modes (0 to 6) can be easily modelled by polynomial functions of m_N in the neighbourhood of useful m_N. To further improve this result, the role of passive system parameters has been studied. It is show that compliant behaviors at mechanical joints create a new order on the system which leads to a large invariance property in the (ω _N × m_N × λ_O) space. Compliant mechanical joint reduces drastically the preload condition as shown by a lower threshold value for m_N and a lower invariance mode number ( now typically 3) with moreover more precise invariance. These properties open the way to new finite dimension controllers