Flatness-Based Motion Planning and Control Strategy of a 3D Overhead Crane

This paper investigates an advanced control strategy for a three-dimensional overhead crane (3DOC) to address the limitations of traditional control methods in trajectory optimization, disturbance rejection, and robustness. Conventional approaches often fail to provide optimal motion planning that handles all the dynamic constraints of the 3DOC and cannot simultaneously address system uncertainty and external disturbances. Moreover, these methods cannot guarantee the convergence time of the observer and controllers. To fill this gap, we developed a time-optimal motion planning algorithm based on differential flatness theory incorporating dynamic constraints and Control limits. Additionally, a Fixed-Time Extended State Observer (FxTESO) is implemented to estimate states and disturbances in fixed time, and a Terminal Sliding Mode Control (TSMC) ensures robust trajectory tracking. Simulation studies and lab-scale experiments on the 3DOC demonstrate the method's improvements in trajectory optimization, disturbance rejection, and overall performance. Compared to existing control strategies, the proposed framework provides enhanced trajectory accuracy, robustness, and fixed-time disturbance rejection, confirming its effectiveness for 3DOC applications.