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Optimal path planning and control of microscopic devices navigating in fluid environments is essential for applications ranging from targeted drug delivery to environmental monitoring. These tasks are challenging due to the complexity of…

Computational Physics · Physics 2025-06-23 Petr Karnakov , Lucas Amoudruz , Petros Koumoutsakos

Active many-body systems composed of many interacting degrees of freedom often operate out of equilibrium, giving rise to non-trivial emergent behaviors which can be functional in both evolved and engineered contexts. This naturally…

Soft Condensed Matter · Physics 2023-11-29 Sumit Sinha , Vishaal Krishnan , L Mahadevan

The paper proposes novel sampling strategies to compute the optimal path alteration of a surface vessel sailing in close quarters. Such strategy directly encodes the rules for safe navigation at sea, by exploiting the concept of minimal…

Robotics · Computer Science 2022-01-12 Thomas Thuesen Enevoldsen , Christopher Reinartz , Roberto Galeazzi

Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…

Analysis of PDEs · Mathematics 2026-03-19 Rebecca M. Crossley , Carles Falco , Ruth E. Baker

Propulsion at microscopic scales is often achieved through propagating traveling waves along hair-like organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of…

Fluid Dynamics · Physics 2014-06-05 Thomas D. Montenegro-Johnson , Eric Lauga

To find the path that minimizes the time to navigate between two given points in a fluid flow is known as Zermelo's problem. Here, we investigate it by using a Reinforcement Learning (RL) approach for the case of a vessel which has a slip…

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…

Finding the best strategy to minimize the time needed to find a given target is a crucial task both in nature and in reaching decisive technological advances. By considering learning agents able to switch their dynamics between standard and…

We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…

Robotics · Computer Science 2020-10-19 Bachir El Khadir , Jean Bernard Lasserre , Vikas Sindhwani

Active navigation in disordered media depends on a biased random walk interacting with environmental constraints. Using E. coli chemotactic navigation in agar gels as a model system, we reveal a fundamental trade-off between diffusive…

Soft Condensed Matter · Physics 2025-12-23 Yang Bai , Caiyun He , Weirong Liu , Songtao Cheng , Pan Chu , Liang Luo , Chenli Liu , Xiongfei Fu

Navigating toward a known target in a noisy environment is a fundamental problem shared across biological, physical, and engineered systems. Although optimal strategies are often framed in terms of continuous, fine-grained feedback, we show…

Statistical Mechanics · Physics 2025-12-24 Abhijit Sinha , Sandeep Jangid , Tridib Sadhu , Shankar Ghosh

Finding an optimum strategy to reach a certain destination by swimming in a background flow is an interesting question which leads to non-trivial results and swimming paths. Here we consider different strategies for various types of surface…

Classical Physics · Physics 2023-08-02 Amir Aghamohammadi , Cina Aghamohammadi , Saman Moghimi-Araghi

When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed-accuracy trade-offs.…

Statistical Mechanics · Physics 2025-09-19 Francesco Mori , L. Mahadevan

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…

Optimization and Control · Mathematics 2021-11-19 Cole Miles , Alexander Vladimirsky

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

We present a novel particle filtering framework for continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows reformulating the estimation…

Optimization and Control · Mathematics 2021-10-08 Qinsheng Zhang , Amirhossein Taghvaei , Yongxin Chen

Cells swimming in viscous fluids create flow fields which influence the transport of relevant nutrients, and therefore their feeding rate. We propose a modeling approach to the problem of optimal feeding at zero Reynolds number. We consider…

Fluid Dynamics · Physics 2011-10-19 Sébastien Michelin , Eric Lauga

Artificial microswimmers are a new technology with promising microfluidics and biomedical applications, such as directed cargo transport, microscale assembly, and targeted drug delivery. A fundamental barrier to realising this potential is…

Fluid Dynamics · Physics 2018-06-27 Thomas D. Montenegro-Johnson

As the length scales of the smallest technology continue to advance beyond the micron scale it becomes increasingly important to equip robotic components with the means for intelligent and autonomous decision making with limited…

Soft Condensed Matter · Physics 2022-09-08 Paul A. Monderkamp , Fabian Jan Schwarzendahl , Michael A. Klatt , Hartmut Löwen

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…

Soft Condensed Matter · Physics 2022-10-12 Suraj Shankar , Vidya Raju , L. Mahadevan