Minimum time-energy trajectory planning for automatic ship berthing

A ship optimal trajectory planning method based on the dynamic model of the ship is presented. First a mathematical modular model is introduced for describing the non-linear dynamics of the ship. Then the problem of optimal trajectory planning is discussed. The trajectory is obtained through the optimization of a time-energy criterion, taking into account constraints on the steering system, environment, non-linearities, and non-convexity of the state space equations. The discrete augmented Lagrangian approach is used to compute the optimal constrained controller. The method was programmed on a HP700 workstation. This approach was applied to automatic ship berthing maneuver