Multi-objective Trajectory Planning with State Constraints for 5-DOF Underactuated Tower Crane Systems

In the practical applications of tower cranes, to improve work efficiency, it is needed to simultaneously rotate the jib, move the trolley, and change the rope length during transportation; however, there exist few control methods for such 5-DOF tower crane systems. In addition, it is still open how to find a balance among reducing the transportation time, saving the energy consumption, and guaranteeing satisfactory transient performance at the same time. Therefore, to address the above issues, in this paper, a multi-objective trajectory planning strategy with state constraints is proposed for 5-DOF tower cranes, which is the first solution that can achieve Pareto optimality of the transportation time and energy consumption, and can simultaneously satisfy all the practical constraints of the state variables and their corresponding velocities. The positioning and anti-swing performance of the planned trajectories are realized by differential flat outputs construction and B-spline curves design; also the multi-objective optimization problem is solved by the improved nondominated neighbor immune algorithm (NNIA). Finally, simulations are carried out for effectiveness verification.