Minimum-Time Control of a Crane with Simultaneous Traverse and Hoisting Motions

The problem of the minimum-time control of a crane having simultaneous traverse and hoisting motions is considered. We propose an approach that converts this problem into a finite-dimensional optimization problem via control parametrization with an appropriate basis function. Such an approach simplifies the treatment of the constraints and allows for the easy satisfaction of the endpoint constraints. This optimization problem is solved using a novel two-stage optimization process. Under additional conditions, the solution obtained from this process can be shown to be the optimum. When these conditions are not met, a near-optimal solution is obtained. Several numerical examples are provided, including the case where there is unequal cable length at the endpoints. The validity of the solution is verified experimentally on a test rig.