Differential-flatness-based finite-time anti-swing control of underactuated crane systems

In this paper, we consider the finite-time regulation controller for the underactuated crane systems in 2-dimensional (2D) space with both constant cable length and varying cable length. The differential-flatness-based approach is applied to the development of finite-time control laws. The elegantly designed controller can simultaneously suppress the payload swing and regulate the trolley to the desired destination within a finite time 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 used 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.