A novel optimal trajectory planning method for overhead cranes with analytical expressions

In this paper, we present a novel time-optimal off-line trajectory planning method with an analytical expression for 2-dimensional (2-D) underactuated overhead cranes. Different from existing methods that analyze the coupling behavior directly, a flat output of this system is constructed to deal with the coupling between the payload swing and trolley motion, based on the differential flatness theory. Next, considering the continuity and smoothness characteristics of B-splines, the trajectory is parameterized to a B-spline curve with unknown parameters to be optimized. Various constraints, including lower and upper swing angle bounds and allowable trolley acceleration, are taken into consideration to optimize the parameters using a polynomial based scheme. Finally, some simulation and experiment results are given to illustrate the satisfactory performance of the proposed method.