Nonlinear time-optimal trajectory planning for varying-rope-length overhead cranes

Purpose From practical perspectives and to improve the working efficiency, trolley transportation and payload hoisting/lowering should be simultaneously controlled. Moreover, in practical crane applications, the transportation time is an important criterion for improving transportation efficiency. Based on these requirements, this paper aims to solve positioning and antiswing control problems and shorten the transportation time for underactuated varying-rope-length overhead cranes. Design/methodology/approach By choosing trolley acceleration and varying-rope-length acceleration as system inputs, the crane system dynamic model is converted into an equivalent model without linearizing/approximating. Then, based on the converted model and system state constraints, a time-optimal problem is formulated. Further, the original problem is converted into an optimization problem with algebraic constraints which can be conveniently solved. Finally, by solving the optimization problem, the optimal trajectories of system states, including displacements, velocities and accelerations, are obtained. Findings This paper first provides a nonlinear time-optimal trajectory planner for varying-rope-length overhead cranes, which achieves accurate and fast trolley positioning and eliminates payload residual swings. Meanwhile, all system states satisfy the given constraints during the entire process. Hardware experimental results show that the proposed time-optimal planner is effective and has better performance compared with existing methods. Originality/value This paper proposes a time-optimal trajectory planner for overhead crane systems with hoisting/lowering motion. The proposed planner achieves fast trolley positioning and eliminates payload residual swing with all the system states being constrained within given scopes. The planner is presented based on the original nonlinear system dynamics without linearization/approximation.