Trajectory planning for overhead crane by trolley acceleration shaping

This paper proposes a novel off-line trolley trajectory planning method for underactuated overhead cranes. The proposed technique is feasible and efficient for overhead crane operation. Dynamic coupling between trolley motion and payload swing was successfully exploited using a staircase form of trolley acceleration. The payload swings in the constant velocity phase were efficiently suppressed and the trolley reached the desired position using this technique. The reasonable number of stairs can be determined by evaluating the residual oscillation amplitude according to the number of stairs and variation in the natural frequency of the pendulum. The proposed approach was first simulated from the kinematics viewpoint to verify the validity of the trolley trajectory and the swing angle of the payload. The proposed approach was then combined with the dynamics of the overall crane, wherein the robust sliding mode controller was applied to ensure that the trolley tracks the designed trajectory. The numerical simulation results demonstrated superior performance and robustness against parameter uncertainties of the proposed method. The proposed method exhibited potential for application in the control of underactuated systems, such as overhead cranes, single-link flexible-joint manipulators, and flexible Cartesian manipulators.