Hydrodynamics can determine the optimal route for microswimmer navigation

As compared to the well explored problem of how to steer a macroscopic agent, like an airplane or a moon lander, to optimally reach a target, optimal navigation strategies for microswimmers experiencing hydrodynamic interactions with walls and obstacles are far-less understood. Here, we systematically explore this problem and show that the characteristic microswimmer-flow-field crucially influences the navigation strategy required to reach a target in the fastest way. The resulting optimal trajectories can have remarkable and non-intuitive shapes, which qualitatively differ from those of dry active particles or motile macroagents. Our results provide insights into the role of hydrodynamics and fluctuations on optimal navigation at the microscale, and suggest that microorganisms might have survival advantages when strategically controlling their distance to remote walls. While control theory for optimal navigation is relevant across scales, from aeronautics to targeted drug delivery, the role of thermal fluctuations and hydrodynamic interactions with interfaces, walls and obstacles at the microscale remains an open question. Here, the authors explore optimal microswimming in the presence of walls or obstacles, and study how hydrodynamic microswimmer-wall interactions impact on optimal microswimming strategies.