A suppress-excite approach for online trajectory generation of uncertain motion systems

We present a framework that allows designing point-to-point closed-form trajectories and identifying flexible modes, jointly. The impulse response of a k-cascaded second-order notch filter is altered by composing it with a polynomial function of even degree in the time domain. The filter impulse response parameters are designed based on the available prior knowledge about the lightly-damped uncertain modes of the driven stage. The resulting chirps signals suppress the response of these oscillatory modes within selected suppression bands in the frequency domain. To check for unknown flexible modes within any desired frequency intervals of interest, the complement of the suppression bands is excited using excitation chirps signals. Using transmissibility, then the frequencies associated with the unknown flexible modes are identified, and the k-cascaded notch filter is updated accordingly. This update process may involve optimizing the parameters of the original filter, or the new filter when the order k changes. Also, real-time trajectory extrapolation is guaranteed under the proposed framework by the simple calculations required. The effectiveness of the proposed framework is illustrated through a numeric simulation example where the integration of both kinematic and dynamic constraints gives rise to the notion of kinodynamical trajectories.