Optimal trajectory planning and tracking control method for overhead cranes

In this study, a novel time-optimal off-line trajectory planning method, together with a tracking controller, is proposed for a two-dimensional (2D) underactuated overhead crane. Specifically, based on the differential flatness technique, a flat output of the system is firstly defined to deal with the coupling between the payload swing and trolley motion, whose trajectory is parameterised to be a B-spline curve with unknown parameters when considering the continuity and smoothness requirements. Various constraints, including swing bound, allowable trolley acceleration, and so on, are then taken into consideration to convert the parameters determination task into an optimisation problem, with the solution employed to construct a high-efficient trolley trajectory with an analytical expression. To enhance tracking performance, a non-linear tracking control law is subsequently designed based on the feedback linearisation technique, whose performance is ensured with theoretical analysis. Finally, some simulation and experimental results are included to demonstrate that the proposed trajectory planning/tracking scheme achieves satisfactory performance for underactuated cranes.