Quentin Brateau

Reliable state estimation for autonomous systems in structured environments frequently depends on acoustic and ultrasonic range sensors. Unlike high-resolution LiDAR, these sensors possess a significant angular aperture, where the measurement follows a first echo principle returning the minimum distance to any obstacle within a sensing cone. This measurement model introduces non-differentiable “min” operators that are inherently difficult to handle with classical probabilistic filters like the Extended Kalman Filter (EKF). This paper proposes a guaranteed state estimation framework based on the remoteness constraint, originally introduced as an inclusion test but limited by computational inefficiency. We present an implementation of the Remoteness Separator within the framework of separator algebra, enabling the use of efficient contraction techniques to prune the state space. A core contribution of this work is the derivation of an efficient implementation which does not generate fake boundaries, thus maintaining the topological integrity of the solution set and enhancing computational performance. The approach is evaluated through a state estimation benchmark in a structured environment, providing a mathematically guaranteed enclosure of the robot’s pose. This implementation is restricted to the two-dimensional case with obstacle segments, but the underlying principles could be extended to more complex geometries and higher dimensions.

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.

Navigating Autonomous Underwater Vehicles (AUVs) presents significant challenges due to the absence of traditional localization systems. Cycle navigation emerges as a promising paradigm, enabling reliable navigation using minimal exteroceptive measurements. This approach leverages predefined cyclic trajectories, which are stabilized based on environmental feedback, ensuring frugal and discreet operations without reliance on high computational power or extensive sensor systems. This work aims to prove the stability of the cycle navigation. As cycle navigation is a non-linear system governed by a discrete inclusion condition, conventional methods have trouble to prove its stability. For this reason, this paper focuses on set methods to prove the stability of cycle navigation. The stability is proven by exhibiting a positive invariant set, which is a set stable by application of the evolution function of the system. This ensures that the evolution function will not remove states from the positively invariant set. Then, the characterization of the capture basin is an asset when performing cycle navigation, as it represents the set of initial states for the system which leads to the positive invariant set. Once the system reaches either the capture basin or the positive invariant set, which are generalized as a capture set, it remains captured forever. This approach not only guarantees the stability of the system in the neighborhood of the equilibrium point, but also establishes that it exists an area in which the stability of the cycle navigation will lead to a stable behavior. This work offers a robust, computationally efficient alternative to traditional stability methods, particularly suited for resource-constrained AUVs, because the underwater environment lacks suitable, cheap and easy-to-use localization methods, which forces us finding alternative ways to navigate and explore this particular environment.