We design new navigation strategies for travel time optimization of microscopic self-propelled particles in complex and noisy environments. In contrast to strategies relying on the results of optimal control theory or machine learning approaches, implementation of these protocols can be done in a semi-autonomous fashion, as it does not require control over the microswimmer motion via external feedback loops. Although the strategies we propose rely on simple principles, they show arrival time statistics strikingly close to optimality, as well as performances that are robust to environmental changes and strong fluctuations. These features, as well as their applicability to more general optimization problems, make these strategies promising candidates for the realization of optimized semi-autonomous navigation.
Optimal navigation in complex environments is a problem with multiple applications ranging from designing efficient search strategies to engineering microscopic cargo delivery. When motion happens in presence of strong external forces, route optimization is particularly important as active particles may encounter trapping regions that would substantially slow down their progress. Here, considering a self-propelled agent moving at a constant speed, we study the efficiency of Zermelo’s classical solution for navigation in a sinusoidal potential landscape. Investigating both cases of motion on the plane and on curved surfaces, we focus on the regime where the external force exceeds self-propulsion in finite regions. There, we show that, despite the fact that most trajectories following the trivial policy of going straight get arrested, the Zermelo policy allows for a comprehensive exploration of the environment. However, our results also indicate an increased sensitivity of the Zermelo strategy to initial conditions, which limits its robustness and long-time efficiency, particularly in presence of fluctuations. These results suggest an interesting trade-off between exploration efficiency and stability for the design of control strategies to be implemented in real systems.
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