Physics-informed identification of an ill-conditioned velocity-coupled roll model for sailboats

Accurate roll modeling is important for unmanned sailboat analysis as sail-induced heeling, appendage loading, and sailing-state-dependent hydrodynamic effects all influence stability and performance. Simplified roll models are easier to identify, but they generally represent these coupled effects through lumped coefficients, limiting physical interpretability. This paper investigates whether a Fossen-type velocity-coupled roll model can be identified under simple excitation despite an ill-conditioned inverse problem. The method combines free-decay observations with static heel-equilibrium data at different wing-sail angles. Static data constrain parameter directions weakly informed by free decay, while parameter scaling based on the Fisher information matrix (FIM) and the two-stage physics-informed training strategy improve optimization stability. Numerical success requires all four parameter errors below 5%. Static data improve practical identifiability; two-stage training raises the success rate from 50% to 90%. In pool tests, static data support plausible parameter estimates, and two-stage training improves repeatability. Static-data configurations show lower and less variable sea-trial heel errors than dynamic-only configurations. In sea trials, using sailing velocities instead of zero velocities reduces quasi-steady heel-prediction RMSE from 4.61° to 2.27° in free sailing and from 3.33° to 1.78° in waypoint traversal. The velocity-coupled model therefore retains physical detail while remaining practically identifiable under the conditions considered.