Robust double-loop trajectory planning with real-time compensation for overhead cranes under external disturbances

In recent years, effective control methods for underactuated systems of bridge cranes have garnered significant attention. However, designing trajectories that ensure both transient performance and resilience to external disturbances is challenging due to crane characteristics and interference. This paper presents a double-loop feedback compensation trajectory planning approach. An initial conditional trajectory is designed based on a smoothing factor. Subsequently, this trajectory is refined into a final reference trajectory with real-time compensation to enhance its response to adversarial perturbations. An online trajectory optimizer is developed using differential flatness theory, addressing second derivative interference from compensation and improving transient performance by considering the system’s payload shift and payload swing energy relations. The integration of the reference trajectory with the optimizer enables real-time adjustments to trolley displacement to counteract external interferences caused by adverse weather conditions. Experiments verify the method’s 0.01-s trajectory generation and 3-s stabilization under various disturbances without residual swing, demonstrating superior real-time robustness.