Optimal trajectory planning strategy for underactuated overhead crane with pendulum-sloshing dynamics and full-state constraints

Complex pendulum-sloshing dynamics induced with specific payloads such as the suspension liquid container increase incredibly the difficulty of the anti-swing control for overhead cranes. Especially, it would be a greater challenge for anti-swing control with simultaneously considering the transportation time and the energy consumption while guaranteeing actuated/unactuated states constraints. In this paper, an optimal trajectory planning strategy for overhead crane with pendulum-sloshing dynamics is proposed by taking transportation time, the energy consumption and full-state constraints into account. First, the dynamic model of overhead crane system with pendulum-sloshing effects is established. Then, based on the formulation as a quasi-convex optimization, three optimal trajectory planning strategies including minimum-time trajectory planning (MTTP), minimum-energy trajectory planning (METP) and time-energy optimal trajectory planning (TEOTP) are proposed to suppress the container swing and liquid sloshing simultaneously. In the three trajectory planners, quasi-convex optimization theory is used to guarantee actuated states (trolley acceleration and velocity) and unactuated states (container swing angle and liquid level sloshing displacement) constraints to be satisfied. Finally, numerical simulation and real experiments results prove that the control performance of the proposed optimal trajectory planning strategy is better than existing methods.