Optimal navigation in a noisy environment

Abstract

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 that efficient navigation emerges from a far simpler principle: natural wandering punctuated by intermittent course corrections. Using a controlled robotic platform, active Brownian particle simulations, and scaling theory, we identify a universal trade-off between noise-induced deviation and the finite cost of reorientation, yielding an optimal course correction frequency governed by only a few system parameters. Despite their differing levels of complexity, our experiment and theory collapse onto common quantitative signatures, including first-passage time distribution and non-Gaussian angular dispersion. Our results establish intermittent course-correction as a minimal and robust alternative to continuous feedback, offering a unifying guiding principle for point-to-point navigation in complex environments.