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

Subchan Subchan


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.


Container Crane; Nonlinear Optimal Control; Singular Control; Direct Method

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J. T. Betts., “Survey of numerical methods for trajectory optimization”. Journal of Guidance, Control, and Dynamics, 21(2):193–207, 1998.

J. T. Betts. Practical Methods for Optimal Control Using Nonlinear Programming. SIAM, Philadelphia, 2001.

P. E. Gill, W. Murray, and M. H. Wright., “SNOPT: An SQP algorithm for large scale constrained optimization”. SIAM Journal on Optimization, 12(4):979–1006, 2002.

C. R. Hargraves and S. W. Paris., “Direct trajectory optimization using nonlinear programming and collocation”. Journal Guidance, Control, and Dynamics, 10(4):338– 342, 1987.

O. von Stryk., “User’s guide for DIRCOL – a direct collocation method for the numerical solution of the optimal control problem”. Technische Universität Darmstad. 1999

O. von Stryk and R. Bulirsch., “Direct and indirect methods for trajectory optimization”. Annals of Operations Research, 37(1- 4):357–373, 1992.



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