Nonlinear Online Trajectory Design for Double-Pendulum Overhead Cranes with Time-Varying Rope Lengths

The inputs of practical crane systems are usually the speed signals, which motivates the trajectory planning for overhead cranes. This paper develops a nonlinear online trajectory for the double-pendulum overhead cranes with time-varying rope lengths without considering any linearization or simplification for the model. Output feedback is introduced into the planned trajectory to enhance the antiswing ability. With the proposed trajectory, the trolley displacement and the rope length can converge to the desired values asymptotically while the double-pendulum effect is eliminated, which is proven by Lyapunov techniques and LaSalle’s invariance theorem. Numerical simulation is carried out to demonstrate the antiswing capability of the proposed method, especially in the cases of parameter variations and disturbed feedback of the swing angles.