Phase plane analysis based motion planning for underactuated overhead cranes

Inspired by the desire to achieve fast payload transportation as well as sufficient swing suppression, a novel phase plane based motion planning method is proposed for underactuated overhead cranes. Specifically, the variation law of the underactuated system states in the phase plane is firstly derived via mathematical analysis for the phase portraits. Based on this, an analytical three-segment acceleration trajectory (namely, a trapezoid velocity trajectory) with the coupling behavior being taken into consideration is obtained under actual crane control constraints. To deal with the jerk (discontinuity) problem, we then present two modified acceleration trajectories by introducing some transition stages and performing some rigorous analysis. Moreover, the trajectories generated by the proposed method can evaluate the maximum payload swing and the arrival time for a given transportation task in advance, which provides essential control indexes for crane operation. Simulation results are provided to illustrate the superior performance of the proposed trajectory planning method.