Direct solutions for robust vibration suppression through motion design

Motion planning is an effective tool for the suppression of residual oscillation in underactuated mechanical systems, and in particular, model-based method can be used to virtually eliminate any unwanted oscillation after the completion of a motion task. Here, a novel motion planning method, aimed at maximizing robustness to model uncertainties and based on a direct formulation, is proposed and tested. The choice of a direct formulation is aimed at overcoming the numerical problems often encountered when dealing with indirect trajectory planning methods, including the limited robustness to any model-plant mismatch. The proposed direct method is based on three different motion profiles, and is tested for the rest-to-rest motion of a slender beam, with and without parametric robustness constraints, but the same framework can be adapted to countless other situations and formulations. The experimental results showcase good accuracy and a sensible improvement in mitigating the effects of unmodeled perturbations on the system sported by the proposed robustified method over its non-robust counterpart. Experimental results show also the outcome is very similar to the one resulting from a more numerically challenging solution formulated as an indirect problem by means of a two-point boundary value problem.