Trajectory Planning and Fixed-time Sliding Mode Tracking Control for Underactuated Crane Systems

In this paper, a composite control scheme is proposed to solve the problems of precise positioning and load swing suppression often encountered in the practical application of an underdriven axle crane. The proposed scheme combines time-optimal trajectory planning with a fixed-time sliding mode tracking controller. Firstly, trigonometric polynomials are used to design a time-optimal trajectory, which can not only ensure that the load is driven to the desired position accurately and quickly, but also restrict the state variables to a specific range. Secondly, a fixed-time sliding mode tracking controller is proposed to ensure that the crane can track the given trajectory accurately and quickly. The controller can make the sliding mode variables converge to a small domain of zero in a fixed time, and then the tracking error will converge to zero. Simulation results show that the proposed composite control strategy performs well in terms of precise positioning and load swing suppression.