Abstract: In view of the problem of an under actuated overhead crane’s payload swing caused by the inertia force, the trajectory planning of trolley was put forward to suppress the payload residual swing. The dynamic model of a crane system with damped oscillation was established, the method of phase plane analysis was used to study residual swing of the payload which are affected by the three different acceleration curves of the trolley. The Lyapunov function based on energy control method was used to dynamically design the acceleration curve of the trolley in real time. The simulation results show that the trajectory planning based on energy control method can effectively restrain the residual vibration of the overhead crane, and the acceleration curve of the trolley is smoother. When the trolley acceleration direction are same with the payload swing direction, the larger the trolley’s acceleration is, the faster the payload normalized energy decrease. The proposed control method can suppress the payload swing angle to the allowable value in 7.9s when the initial angle of payload is 0.087 rad.

Key words: under actuated system, trajectory planning, phase plane analysis, residual swing, overhead crane