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Swimming consists by definition in propelling through a fluid by means of bodily movements. Thus, from a mathematical point of view, swimming turns into a control problem for which the controls are the deformations of the swimmer. The aim…

Optimization and Control · Mathematics 2017-02-15 Thomas Chambrion , Laetitia Giraldi , Alexandre Munnier

We address the problem of controlling a dynamical system governing the motion of a 3D weighted shape changing body swimming in a perfect fluid. The rigid displacement of the swimmer results from the exchange of momentum between prescribed…

Optimization and Control · Mathematics 2011-03-30 Thomas Chambrion , Alexandre Munnier

For decades, people have been seeking for fishlike flapping motions that can realize underwater propulsion with low energy cost. Complexity of the nonstationary flow field around the flapping body makes this problem very difficult. In…

Robotics · Computer Science 2023-06-28 Jin Zhang , Lei Zhou , Bochao Cao

This work aims at finding optimal navigation policies for thin, deformable microswimmers that progress in a viscous fluid by propagating a sinusoidal undulation along their slender body. These active filaments are embedded in a prescribed,…

Fluid Dynamics · Physics 2023-02-13 Zakarya El Khiyati , Raphael Chesneaux , Laetitia Giraldi , Jeremie Bec

We apply a reinforcement learning algorithm to show how smart particles can learn approximately optimal strategies to navigate in complex flows. In this paper we consider microswimmers in a paradigmatic three-dimensional case given by a…

Fluid Dynamics · Physics 2018-04-30 K. Gustavsson , L. Biferale , A. Celani , S. Colabrese

In this paper we study the locomotion of a shape-changing body swimming in a two-dimensional perfect fluid of infinite extent. The shape-changes are prescribed as functions of time satisfying constraints ensuring that they result from the…

Optimization and Control · Mathematics 2009-10-29 Thomas Chambrion , Alexandre Munnier

Smart active particles can acquire some limited knowledge of the fluid environment from simple mechanical cues and exert a control on their preferred steering direction. Their goal is to learn the best way to navigate by exploiting the…

Fluid Dynamics · Physics 2018-05-02 Simona Colabrese , Kristian Gustavsson , Antonio Celani , Luca Biferale

Navigation in turbulent environments is a fundamental challenge for biological and artificial microswimmers. While most existing studies focus on adapting motility or steering, the role of active morphological changes in navigation remains…

Motile microorganisms develop effective swimming gaits to adapt to complex biological environments. Translating this adaptability to smart microrobots presents significant challenges in motion planning and stroke design. In this work, we…

Robotics · Computer Science 2025-06-03 Yuyang Lai , Sina Heydari , On Shun Pak , Yi Man

This study investigates a method to guide and control fish schools using virtual fish trained with reinforcement learning. We utilize 2D virtual fish displayed on a screen to overcome technical challenges such as durability and movement…

Robotics · Computer Science 2026-03-18 Yusuke Nishii , Hiroaki Kawashima

Swimming organisms can escape their predators by creating and harnessing unsteady flow fields through their body motions. Stochastic optimization and flow simulations have identified escape patterns that are consistent with those observed…

Fluid Dynamics · Physics 2021-09-29 Ioannis Mandralis , Pascal Weber , Guido Novati , Petros Koumoutsakos

In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots…

Analysis of PDEs · Mathematics 2012-03-19 Jérôme Lohéac , Alexandre Munnier

In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic…

Optimization and Control · Mathematics 2014-04-25 Gianni Dal Maso , Antonio DeSimone , Marco Morandotti

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyse this navigation by combining deep reinforcement learning with direct numerical…

Fluid Dynamics · Physics 2023-06-21 Krongtum Sankaewtong , John J. Molina , Matthew S. Turner , Ryoichi Yamamoto

Marine microorganisms must cope with complex flow patterns and even turbulence as they navigate the ocean. To survive they must avoid predation and find efficient energy sources. A major difficulty in analysing possible survival strategies…

Fluid Dynamics · Physics 2022-11-29 J. Qiu , N. Mousavi , K. Gustavsson , C. Xu , B. Mehlig , L. Zhao

We establish through numerical simulation conditions for optimal undulatory propulsion for a single fish, and for a pair of hydrodynamically interacting fish, accounting for linear and angular recoil. We first employ systematic 2D…

Fluid Dynamics · Physics 2017-04-05 Audrey P. Maertens , Amy Gao , Michael S. Triantafyllou

Efficient point-to-point navigation in the presence of a background flow field is important for robotic applications such as ocean surveying. In such applications, robots may only have knowledge of their immediate surroundings or be faced…

Elongate animals and robots use undulatory body waves to locomote through diverse environments. Geometric mechanics provides a framework to model and optimize such systems in highly damped environments, connecting a prescribed shape change…

Robotics · Computer Science 2025-10-21 Jianfeng Lin , Tianyu Wang , Baxi Chong , Matthew Fernandez , Zhaochen Xu , Daniel I. Goldman

Aquaculture systems can benefit from the recent development of advanced control strategies to reduce operating costs and fish loss and increase growth production efficiency, resulting in fish welfare and health. Monitoring the water quality…

Systems and Control · Electrical Eng. & Systems 2023-06-19 Fahad Aljehani , Ibrahima N'Doye , Taous-Meriem Laleg-Kirati

We study the fluid dynamics of two fish-like bodies with synchronised swimming patterns. Our studies are based on two-dimensional simulations of viscous incompressible flows. We distinguish between motion patterns that are externally…

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