Transportation task-oriented trajectory planning for underactuated overhead cranes using geometric analysis

The authors present a novel off-line trolley trajectory planning method for the payload horizontal transferring task of underactuated overhead cranes. The proposed approach is feasible and efficient for crane control. Specifically, the coupling behaviour between the actuated trolley motion and the unactuated payload swing is successfully addressed via some rigorous geometric analysis in the phase plane. Based on this, an analytical three-segment acceleration trajectory (i.e. a trapezoid velocity trajectory) is firstly obtained by carefully considering the practical constraints of crane control. To tackle the infinite jerk (discontinuity) problem as well as to show the flexibility of the proposed geometric analysis-based method, the authors then introduce some transition mechanisms to smoothen the acceleration trajectory, and to construct two types of modified acceleration trajectories. For any given transferring task, the proposed trajectory planning approach provides a novel mechanism to determine the parameters of the trajectories so that the transportation indexes, including the permitted payload swing, transferring efficiency and so on, can be met without much difficulty. Both simulation and experimental results are exhibited to illustrate the effectiveness and feasibility of the proposed approach.