# Optimal control of point-to-point navigation in turbulent time-dependent flows using Reinforcement Learning

arXiv: https://arxiv.org/abs/2103.00329 · HTML: https://mlsanity.com/paper/2103.00329/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 27 Feb 2021.

## Builds on (most cited first, 3 of 3)

- [Flow Navigation by Smart Microswimmers via Reinforcement Learning](https://mlsanity.com/paper/1701.08848/) (2017)
- [Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning](https://mlsanity.com/paper/1907.08591/) (2019)
- [Finding Efficient Swimming Strategies in a Three Dimensional Chaotic Flow by Reinforcement Learning](https://mlsanity.com/paper/1711.05826/) (2017)

## Built on by (most cited first, 6 of 6)

- [Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction](https://mlsanity.com/paper/2307.11793/) (2023)
- [Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policies](https://mlsanity.com/paper/2403.15267/) (2024)
- [HypeRL: Hypernetwork-Based Reinforcement Learning for Control of Parametrized Dynamical Systems](https://mlsanity.com/paper/2501.04538/) (2025)
- [Taming Lagrangian Chaos with Multi-Objective Reinforcement Learning](https://mlsanity.com/paper/2212.09612/) (2022)
- [Deep Dive into Model-free Reinforcement Learning for Biological and Robotic Systems: Theory and Practice](https://mlsanity.com/paper/2405.11457/) (2024)
- [Physics-enhanced reinforcement learning for real-time optimal control of dynamical systems](https://mlsanity.com/paper/2607.16177/) (2026)

## Abstract (arXiv)

We present theoretical and numerical results concerning the problem to find the path that minimizes the time to navigate between two given points in a complex fluid under realistic navigation constraints. We contrast deterministic Optimal Navigation (ON) control with stochastic policies obtained by Reinforcement Learning (RL) algorithms. We show that Actor-Critic RL algorithms are able to find quasi-optimal solutions in the presence of either time-independent or chaotically evolving flow configurations. For our application, ON solutions develop unstable behavior within the typical duration of the navigation process, and are therefore not useful in practice. We first explore navigation of turbulent flow using a constant propulsion speed. Based on a discretized phase-space, the propulsion direction is adjusted with the aim to minimize the time spent to reach the target. Further, we explore a case where additional control is obtained by allowing the engine to power off. Exploiting advection of the underlying flow, allows the target to be reached with less energy consumption. In this case, we optimize a linear combination between the total navigation time and the total time the engine is switched off. Our approach can be generalized to other setups, for example, navigation under imperfect environmental forecast or with different models for the moving vessel.