A pseudospectral time-optimal motion planner for underactuated overhead crane systems

In this paper, we present a pseudospectral time-optimal motion planning technique for underactuated overhead crane systems. Various practical constraints, including the lower and upper bounds for the harmful payload swing, the cart/trolley velocity, acceleration and jerk, are all taken into account in the proposed approach. Different with existing approaches that rely heavily on the linearized model around the equilibrium point, the Guass pseudospectral method (GPM) is adopted to convert the original time-optimal problem into a parametric nonlinear programming problem (NLP), for which both the nonlinear dynamics and various constraints can be successfully considered simultaneously. Extensive comparative simulation results are presented to demonstrate the superior performance of the proposed approach. It should be remarked that, the results provide some practically meaningful performance limits for automatic or manual operation of the crane systems in transportation-oriented tasks.