Stochastic Optimal Control of a Sailboat

TL;DR

This paper develops an accelerated semi-Lagrangian method for stochastic optimal control of sailboats, improving computational efficiency and accuracy in path planning under unpredictable wind conditions.

Contribution

It introduces a reduced state space, adaptive timestep discretization, and an improved tack-switching operator for hybrid stochastic control problems in sailing.

Findings

Significant speed-up in computational time.

Enhanced accuracy in tack-switching decisions.

Effective handling of stochastic wind variations in simulations.

Abstract

In match race sailing, competitors must steer their boats upwind in the presence of unpredictably evolving weather. Combined with the tacking motion necessary to make upwind progress, this makes it natural to model their path-planning as a hybrid stochastic optimal control problem. Dynamic programming provides the tools for solving these, but the computational cost can be significant. We greatly accelerate a semi-Lagrangian iterative approach of Ferretti and Festa (R. Ferretti and A. Festa, "Optimal Route Planning for Sailing Boats: A Hybrid Formulation", J Optim Theory Appl (2019)) by reducing the state space dimension and designing an adaptive timestep discretization that is very nearly causal. We also provide a more accurate tack-switching operator by integrating over potential wind states after the switch. The method is illustrated through a series of simulations with varying stochastic wind conditions.