Fast and save container cranes as bilevel optimal control problems

For the use of container cranes in high rack warehouses, reference trajectories can be obtained from optimal control problems in order to control the swinging of the crane system during the fast movement and in order to reach an equilibrium position at the end of the trajectory. Safety requirements extend these problems to bilevel optimal control problems, where the existence of alternative stop trajectories has to be guaranteed. A method as to how these complex problems can be reduced to conventional optimal control problems, even under control and state constraints, is presented together with numerical examples.