Optimal navigation strategies for active particles

Abstract

The quest for the optimal navigation strategy in a complex environment is at the heart of microswimmer applications like cargo carriage or drug targeting to cancer cells. Here, we formulate a variational Fermat's principle for microswimmers determining the optimal path regarding travelling time, energy dissipation or fuel consumption. For piecewise constant forces (or flow fields), the principle leads to Snell's law, showing that the optimal path is piecewise linear, as for light rays, but with a generalized refraction law. For complex environments, like general 1D-, shear-or vortex-fields, we obtain exact analytical expressions for the optimal path, showing, for example, that microswimmers sometimes have to temporarily navigate away from their target to reach it fastest. Our results might be useful to benchmark algorithmic schemes for optimal navigation. * liebchen@hhu.de; equal contributions † hloewen@hhu.de; equal contributions arXiv:1901.08382v1 [cond-mat.soft]

Zermelo’s problem: Optimal point-to-point navigation in 2D turbulent flows using reinforcement learning

“…In this case, a navigation protocol based on (3) would be unstable for all practical purposes. This is most likely the reason why previous works on ON have dealt mainly with simple advecting flow configurations [21,29,30].…”

“…The main drawback is that they might be distributed in a non-optimal way, as they might accumulate in uninteresting regions, or disperse away from key points. Beside this applied motivation, the problem of (time) optimal point-to-point navigation in a flow, known as Zermelo's problem [18], is interesting per se in the framework of Optimal Control Theory [19][20][21][22].…”

“…The large-scale periodicity of the underlying flow is L, and we fixed δ = L/10. the best of our knowledge, only simple advecting flows have been studied so far for both ON [21,29,30] and RL [30].…”

Autonomous navigation of shape-shifting microswimmers

“…Recent advances in combining active colloids and stimuliresponsive materials should provide a promising platform to apply the design principles outlined here [28]. Looking forward, autonomous navigation based on internal degrees of freedom could be combined with external control strategies [29]…”

Efficient Navigation of Colloidal Robots in an Unknown Environment via Deep Reinforcement Learning

“…In potential real‐world applications (e.g., nanodrug delivery, precision surgery, environmental remediation, and machines), micro‐/nanorobots are confronted with navigation challenges, including long‐distance travel (e.g., travel in tissue, soil, and vasculature), unknown or spatiotemporally changing environment abundant with obstacles and dead ends, and additional time and fuel constraints. Beyond developing sophisticated micro‐/nanorobot systems that have more efficient transport mechanisms and sensing capabilities, efforts have also been directed toward developing better navigation strategies . Examples include the application of a Markov decision process framework and a variational Fermat's principle to compute optimal navigation paths in mazes and flow fields.…”