On broaching-to prevention using optimal control theory with evolution strategy (CMA-ES)

Broaching-to, an uncontrollable maneuvering problem that may occur in following and quartering seas, can induce large roll motion and sometimes capsizing due to violent yaw motions, e.g., Nicholson (Some Parametric Model Experiment to Investigate Broaching-to, pp 160–166, 1974). Broaching-to arises when a ship cannot maintain its desired course even under maximum steering effort. Previous experiments and numerical simulations of the broaching-to phenomenon have applied proportional-derivative (PD) control, which cannot provide the maximum steering effort. To maximize the steering effort, the previous study replaced PD control by optimal control theory by Maki et al. (J Jpn Soc Nav Archit Ocean Eng 7:207–212, 2008) and Maki et al. (J Jpn Soc Nav Archit Ocean Eng 8:115–122, 2008). A case of the ship control, when the ship developed large yaw motions despite the optimal control, was observed. However, because optimization techniques such as the variational method were insufficiently powerful for solving this highly nonlinear problem, the optimization could be performed only around local optima. The aim is to globally seek a better local solution among the numerous local optima. To achieve this goal, the authors applied the Covariance Matrix Adaption Evolution Strategy (CMA-ES), a state-of-the-art algorithm in evolutionary computation for derivative-free continuous optimization. The optimal rudder control for preventing broaching-to is then obtained, and its characteristics are discussed.