Navigation Without Localization Using Stable Cycles

Navigating autonomous robots in GNSS-denied environments, such as underwater, remains a fundamental challenge due to the lack of reliable localization. Classical approaches rely on exteroceptive sensors and complex state estimation pipelines, which are often computationally expensive, not-precise, and unsuitable for stealthy or resource-constrained platforms. In this article, we propose a novel, frugal navigation paradigm based on stable cycles, inspired by biological navigation strategies observed in migratory animals. Our method enables a robot to follow and stabilize a predefined cycle in the environment without requiring explicit state estimation. A timed automaton is used to generate control inputs that drive the robot along a discretized cycle, which is then stabilized in the world frame using sparse environmental measurements. We formally describe this cycle-based control framework, provide a proof of its stability, and validate the approach experimentally on a real robot. This work opens a new direction for low-cost, low-observability robotic navigation in unstructured and GNSS-denied environments.