Motion and anti-swing control of underactuated bridge cranes using differential flatness

The regulation controller is designed for the underactuated crane system in 2-dimensional (2D) space by using a differential-flatness-based approach. The elegantly designed controller can simultaneously suppress the payload swing and regulate the trolley to the desired destination for the 2D bridge crane system in the case of constant cable length. Considering cable length variation, the flatness-based tracking controller is presented meticulously in a separately two-step program. Specifically, the finite-time technique is first applied to achieve the simultaneous motion regulation and payload swing suppression and elimination within a finite time. Then, we propose a Lyapunov-based tracking control method, under which the cable can track a predefined trajectory. Simulation results are provided to demonstrate both the efficiency and the robustness against external disturbances of the addressed control algorithms.