Reducing residual vibration in systems with uncertain resonances

Robots that perform rapid motions tend to excite system resonant frequencies. To perform a sequence of tasks more quickly, the settling time required for the vibration to decay should be minimal. Input functions are derived that produce rapid open-loop moves with greatly reduced residual vibration amplitude. To accommodate errors in the assumed system natural frequency, these forcing function are constructed so that the magnitude of their frequency spectra remains sufficiently small over a range of frequencies that bound the system natural frequency by +or-10%. These input functions are derived as a series expansion of ramped sinusoid functions with coefficients chosen to minimize spectral magnitude in this frequency band. Some simulations are performed to indicate that these functions can reduce residual vibration considerably even when the assumed natural frequency is in error by 10%. These inputs can then serve as the basis for a closed-loop implementation to generate reference trajectories that minimally excite system resonances.<>