Modeling and optimal control of tower crane motions

Abstract

The growing importance of tower cranes is apparent with their more widespread use on construction projects. The automation of tower crane operations is motivated by several factors, such as economic priorities, safety, reliability and speed. The research in this thesis investigates the application of optimal trajectories for tower cranes to improve the performance of their operations.

A dynamic study of a fixed-boom tower crane is initiated. Employing the Lagrangian method, a simplified mathematical description governing crane motion in state-space form is developed. To achieve fast operation with small load swing, the crane optimization problem is formulated as a special case of Lagrange optimal problem with inequality constraints on controls and terminal states. This is further extended to allow free end time and path (trajectory) constraints.

Due to computational difficulties risen in finding optimal load trajectories for general motions using conventional optimization methods, an iterative algorithm is proposed in order to speed up the computation of optimal solutions. The algorithm is based on known second-order methods, which have been adapted and customized here for application to the required crane optimizations.

Finally, the proposed algorithm is successfully tested on the crane optimization problem to find optimal load transfers in two different cases. Comparing with typical load transfers of a conventional tower crane, the optimal load transfers offer significant time saving with limited swing and smooth motions.