[Paper Review] A Hybrid control approach to the route planning problem for sailing boats

Roberto Ferretti, Adriano Festa|arXiv (Cornell University)|Jul 25, 2017

Adaptive Control of Nonlinear Systems14 references3 citations

TL;DR

This paper proposes a stochastic hybrid optimal control framework for route planning in sailing boat races, integrating continuous path optimization with discrete tacking/gybing maneuvers. By modeling wind variability and tacking penalties via viscosity solutions and monotone numerical schemes, the approach yields feedback controls that outperform standard methods in complex, real-world scenarios including obstacles and variable winds.

ABSTRACT

We present an optimal hybrid control approach to the problem of stochastic route planning for sailing boats, especially in short course fleet races, in which minimum average time is an effective performance index. We show that the hybrid setting is a natural way of taking into account tacking/gybing maneuvers and other discrete control actions, and provide examples of increasing complexity to model the problem. Moreover, we carry out a numerical validation of the approach and show that results are in good agreement with theoretical and practical knowledge.

Motivation & Objective

• Address the challenge of optimal route planning in short-course sailing races with stochastic wind conditions.
• Model tacking and gybing maneuvers as discrete control actions within a hybrid dynamical system framework.
• Incorporate wind variability and tacking penalties into a unified optimal control formulation.
• Develop a numerical scheme that ensures convergence and stability for the resulting Hamilton-Jacobi-Bellman equation.
• Validate the approach on realistic scenarios including state constraints (coastlines, obstacles) and variable wind drift/diffusion.

Proposed method

• Formulate the sailing boat dynamics as a stochastic hybrid system with continuous controls (heading) and discrete controls (tack switching).
• Model wind evolution as a stochastic process with drift (average rotation) and diffusion (random fluctuations), using a Markovian approximation.
• Define a cost functional that includes time-to-goal, tacking penalties, and state constraints via penalized velocity.
• Apply dynamic programming to derive the Hamilton-Jacobi-Bellman (HJB) equation for the value function.
• Implement a monotone finite difference scheme for solving the HJB equation, ensuring convergence and stability.
• Use feedback control derived from the value function to generate optimal trajectories without re-solving for new initial conditions.

Experimental results

Research questions

• RQ1 How can discrete tacking maneuvers be effectively modeled within a continuous optimal control framework for sailing route planning?
• RQ2 To what extent does incorporating stochastic wind variability improve the realism and performance of optimal sailing routes?
• RQ3 How do wind drift and diffusion affect optimal strategy in the presence of asymmetric wind rotation?
• RQ4 Can the hybrid control approach handle state constraints such as coastlines and obstacles while maintaining computational efficiency?
• RQ5 How do the computed optimal trajectories compare with theoretical expectations and practical sailing strategies?

Key findings

• The hybrid control approach successfully captures the physical reality of tacking delays and prevents unphysical 'chattering' behavior.
• Optimal trajectories exhibit a preference for the left side of the domain when wind drift is anti-clockwise, consistent with the 'tacking on a lift' strategy.
• With increasing wind drift magnitude, the optimal strategy becomes increasingly asymmetric, favoring regions where favorable wind angles are more likely.
• The presence of coastlines or obstacles modifies the optimal path, forcing avoidance maneuvers and reducing the extremity of the strategy compared to open domains.
• The feedback control law is reusable across different starting points without re-computation, enabling real-time application.
• Numerical validation confirms that the computed solutions align well with theoretical expectations and known sailing practices, especially under varying wind conditions.