With the increasing number of applications for both surface and underwater autonomous vehicles, a great amount of control methods and guidance principles has been developed over the years. This work proposes a review of the most common of these methods. It is mainly focused on model-based nonlinear control methods and guidance principles. Notably, this work details examples and variations of model-based linearizing controllers, applications of line of sight guidance, sliding mode controllers and several other less common control methods for both fully-actuated and underactuated vehicles. Additionally, this work proposes an alternative definition of underactuation with respect to the task allowing for a better understanding of the consequences of underactuation on control. Comparison of fully-actuated and underactuated cases shows how control laws can be used to solve the problems of underactuation and what mechanisms can be used to compensate for the lack of actuation on a degree of freedom. The reviewed methods are compared and discussed with respect to their capabilities, limitations and suitability for typical tasks.

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.