Energy optimal trajectory planning and tracking control for offshore boom cranes

Offshore boom cranes are widely utilized in marine operations. However, their underactuated and nonlinear characteristics make it more difficult to suppress payload swing. Moreover, most existing research neglects the critical energy optimal problem and insufficiently considers state constraints, the velocity constraints of state variables, and input saturation simultaneously. Considering the above challenges, this paper proposes an energy optimal trajectory planning and trajectory tracking method. Specifically, a coordinate transformation is applied to state variables to formulate a new dynamical model. Subsequently, an energy optimal offline trajectory is generated using the symplectic pseudospectral method, facilitating precise payload transportation with effective swing suppression. Then, a symplectic pseudospectral model predictive controller is implemented online to ensure accurate tracking. Additionally, the proposed method ensures operational safety by incorporating a series of constraints, including full state constraints, the velocity constraints of state variables, and input saturation simultaneously. Finally, satisfactory performance of the proposed method is verified through extensive simulations.