Time-Optimal Route Planning for Electric Ships in Stochastic Seas via PMP–HJB Equivalence

초록

We propose an integrated framework for minimum-time return-to-origin routing of electric-propelled ships operating under uncertain wind, waves, and currents, with a particular focus on partial-failure conditions. Because delayed return in harsh seas can escalate operational risk, the framework is designed to deliver not only fast routes but also dependable guidance under forecast and modeling uncertainty. We first generate stochastic metocean profiles using a vector autoregression (VAR) model that preserves cross-variable dependencies, and we couple these profiles with a physics-based vessel model. Wind forcing and wave-added resistance are converted into an equivalent drift and combined with ocean currents, allowing heterogeneous environmental effects to be treated consistently in the routing formulation. The time-optimal route is computed using Pontryagin's Maximum Principle (PMP), and the solution is validated and generalized through the Hamilton-Jacobi-Bellman (HJB) value function, providing a complementary policy-level view of optimality. To quantify operational robustness, we construct a large library of perturbed routes and identify an asymmetric robust corridor in which transit-time inflation remains within a 10% margin. Simulation studies in a realistic coastal scenario show that the proposed approach yields stable minimum-time return routes, clarifies when near-straight paths become fragile, and offers actionable guidance for safe and economical operation. The results support practical deployment in digital-twin and decision-support systems for electric and autonomous surface ships.

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