Robust transient oscillation reduction for rest-to-rest motion of underactuated multibody systems

Conventional model-based design methods are often limited in their effectiveness by model-plant discrepancy. A solution to this problem is proposed in this work to enhance the robustness of motion planning solution for systems affected by parametric uncertainty. The method exploits a variational formulation in the form of a two-point boundary value problem (TPBVP) in which the robustness is achieved as a constraint enforced at the two boundaries. The formulation, which is specifically targeted at underactuated systems, aims at reducing both the transient and residual vibrations, as well as at mitigating the actuation effort. The development of the method is supported by its application to two numerical test-cases in the form of a double pendulum on a cart and a translating flexible beam.