Dynamic modeling and self-tuning anti-sway control of a seven degree of freedom shipboard knuckle boom crane

Abstract

This paper addresses the deficiency of research in anti-sway control for high degree of freedom (DOF) shipboard cranes by developing a dynamic model and anti-sway control system for a seven-DOF shipboard knuckle boom crane, mounted aboard a vessel that experiences six-DOF ship motion. The dynamic model provides fidelity beyond what is typically seen in literature, including the mass and inertia of the hydraulic actuators, sheaves and winch, along with internal actuator dynamics and a realistic cable fall angle. The crane’s kinematics are derived using both the standard transformation matrix approach and with dual quaternions, and the equations of motion obtained with the Lagrange approach. To provide anti-sway control, a self-tuning anti-sway trajectory modifier is combined with a nonlinear sliding mode controller and a nonlinear trajectory optimizer. Tested in simulation on a ship with six-DOF motion at sea state 6, the system with self-tuning disabled provided a 64% reduction in the average root-mean-square-error (RMSE) between the desired and actual payload positions across the x and y trajectories. Allowing the anti-sway trajectory modifier to self-tune provided a 74% reduction in RMSE under the same conditions. When a 5 kN disturbance force was applied to the payload, the system without self-tuning showed a 58% reduction in the average RMSE, while with self-tuning enabled showed a 77% reduction in RMSE. The self-tuning anti-sway control system was also shown to be robust to errors in system parameters, where errors up to ±20% in the simulated crane resulted in a maximum increase of average RMSE of only 6.3%. Within simulation, the anti-sway control system is shown to be highly effective at tracking a time-varying payload trajectory for a seven-DOF knuckle boom crane and reducing undesired payload motion, and is shown to be robust to both sudden disturbances and errors in system parameters.