Optimal navigation strategies for microswimmers on curved manifolds

Abstract

Finding the fastest path to a desired destination is a vitally important task for microorganisms moving in a fluid flow. We study this problem by building an analytical formalism for overdamped microswimmers on curved manifolds and arbitrary flows. We show that the solution corresponds to the geodesics of a Randers metric, which is an asymmetric Finsler metric that reflects the irreversible character of the problem. Using the example of a spherical surface, we demonstrate that the swimmer performance that follows this "Randers policy" always beats a more direct policy. A study of the shape of isochrones reveals features such as self-intersections, cusps, and abrupt nonlinear effects. Our work provides a link between microswimmer physics and geodesics in generalizations of general relativity.

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Cited by in corpus (10)

• Active matter under control: Insights from response theory
• Reinforcement learning of optimal active particle navigation
• Optimal active particle navigation meets machine learning
• Optimal navigation of microswimmers in complex and noisy environments
• Energetic cost of microswimmer navigation: the role of body shape
• Optimal Control in Soft and Active Matter
• Force Dipole Interactions in Tubular Fluid Membranes
• Intrinsic Langevin dynamics of rigid inclusions on curved surfaces
• Kinetic theory of decentralized learning for smart active matter
• Optimal navigation in two-dimensional flows: Control theory and reinforcement learning