Invariant-Based Inverse Engineering of Crane Control Parameters

By applying invariant-based inverse engineering in the small-oscillation regime, we design the time dependence of the control parameters of an overhead crane (trolley displacement and rope length) to transport a load between two positions at different heights with minimal final-energy excitation for a microcanonical ensemble of initial conditions. The analogy between ion transport in multisegmented traps or neutral-atom transport in moving optical lattices and load manipulation by cranes opens a route for a useful transfer of techniques among very different fields.We acknowledge our discussions with S. Martínez-Garaot and M. Palmero. This work was supported by Eusko Jaurlaritza (Grant No. IT986-16); MINECO/ FEDER,UE (Grants No. FIS2015-67161-P and No. FIS2015-70856-P); QUITEMAD+CM S2013- ICE2801; and by Programme Investissements d'Avenir under the program ANR-11-IDEX 0002-02, reference ANR-10-LABX-0037-NEXT