Direct Method of the Minimum-Time Traversing and Hoisting Motion of the Container Crane

Abstract

In this paper, a dynamic model of the container crane which represents simultaneous traversing and hoisting motions is discussed. The model is derived using Lagrangian modeling techniques. The problem is to minimize the transfer time of a container, where the optimal trajectory should satisfy the specified initial and terminal conditions and some constraints. The optimal control problem is transformed into sequence of nonlinear constrained optimization problems by discretising of the state and/or control variables. Numerical examples are provided, including the case where there is a singular-arc on control.