Risk-aware stochastic control of a sailboat

TL;DR

This paper introduces a robust, risk-aware control method for sailboat path planning under stochastic wind conditions, optimizing the probability of timely arrival while accounting for hybrid control dynamics.

Contribution

It develops a novel numerical approach solving quasi-variational inequalities for risk-aware policies applicable to all initial positions and thresholds simultaneously.

Findings

Risk-aware policies outperform risk-neutral ones in timely arrival probability.

The method effectively reduces tack-switches by leveraging wind predictions.

Monte-Carlo simulations validate the robustness of the proposed control strategy.

Abstract

Sailboat path-planning is a natural hybrid control problem (due to continuous steering and occasional "tack-switching" maneuvers), with the actual path-to-target greatly affected by stochastically evolving wind conditions. Previous studies have focused on finding risk-neutral policies that minimize the expected time of arrival. In contrast, we present a robust control approach, which maximizes the probability of arriving before a specified deadline/threshold. Our numerical method recovers the optimal risk-aware (and threshold-specific) policies for all initial sailboat positions and a broad range of thresholds simultaneously. This is accomplished by solving two quasi-variational inequalities based on second-order Hamilton-Jacobi-Bellman (HJB) PDEs with degenerate parabolicity. Monte-Carlo simulations show that risk-awareness in sailing is particularly useful when a carefully calculated bet on the evolving wind direction might yield a reduction in the number of tack-switches.