Simon Rohou

ENSTA Bretagne · Lab-STICC

This paper proposes a new set-membership method for estimating the trajectories of dynamical systems, when the states are completely unknown and only non-linear observations are available. The first part of the proposed method is symbolic and follows the decomposition of Brunovsky, i.e. , it decomposes the set of differential equations describing...

Set-based state estimation procedures have the advantage of enclosing all possible system states under the assumption of bounded measurement uncertainty, the structural correctness of dynamic systems models, and the representation of external disturbances and imperfectly known parameters by finitely large sets. In contrast to stochastic counterpart...

An autopilot is a combination of an INS (Inertial Navigation System), additional predefined sensors, actuators, and communication ports, with control algorithms. Its purpose is to provide the best state estimation of a robot in all conditions as well as autonomous operation such as following waypoints. Some experiments show that recurring causes of...

Set-based state estimation procedures have the advantage of enclosing all possible system states under the assumption of bounded measurement uncertainty, the structural correctness of dynamic systems models, and the representation of external disturbances and imperfectly known parameters by finitely large sets. In contrast to stochastic counterpart...

In this paper, we propose a new approach for improving significantly existing guaranteed integration methods for state equations with uncertain initial conditions. We first find a tube that encloses the solution of the differential equation assuming that the initial state is known. Then, using Lie symmetries, we inflate the tube in order to contain...

Recent advances in computational power, algorithms, and sensors allow robots to perform complex and dangerous tasks, such as autonomous missions in space or underwater. Given the high operational costs, simulations are run beforehand to predict the possible outcomes of a mission. However, this approach is limited as it is based on parameter space d...

For linear time-invariant dynamic systems with exactly known coefficients of their system matrices for which measurements with bounded errors are available at discrete time instants, an optimal polygonal state estimation scheme was recently published. This scheme allows for tightly enclosing all possible state trajectories in presence of uncertain,...

Interval analysis is a numerical tool classically used for solving nonlinear equations in a guaranteed way. It has been shown that it can be used to build reliable nonlinear state estimators for dynamical systems. Numerous simulations inspired from real-life applications have shown the applicability of the approach. This paper proposes to implement...

This paper proposes an interval-based method for estimating the state of a linear continuous-time dynamical system. In this work, we assume that the measurements are provided at discrete times and that all errors are bounded. Interval analysis is used to propagate the interval uncertainties continuously over time. The resulting method is guaranteed...

In this paper, we propose an interval constraint programming approach that can handle the differential-algebraic CSP (DACSP), where an instance is composed of real and functional variables (also called dynamic variables or trajectories) together, and differential and/or “static” numerical constraints among those variables. Differential-Algebraic CS...

The focus of this book is on interval methods for robot localisation. The book presents thoroughly the methodology and illustrates it with examples from underwater robots in unknown environments.

This paper presents a new approach to bounded-error state estimation involving time uncertainties. For a given bounded observation of a continuous-time non-linear system, it is assumed that neither the values of the observed data nor their acquisition instants are known exactly. For systems described by state-space equations, we prove theoretically...

The localization of underwater robots remains a challenging issue. Usual sensors, such as Global Navigation Satellite System (GNSS) receivers, cannot be used under the surface and other inertial systems suffer from a strong integration drift. On top of that, the seabed is generally uniform and unstructured, making it difficult to apply usual Simult...

This paper presents a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points in SLAM methods, especially in homogeneous environments with difficult scenes recognitions. The proposed appr...

This paper proposes a new method for guaranteed integration of state equations. The main idea is to formalize the problem as a constraint network, the variables of which are trajectories defined by arithmetic and differential equations. The contribution of the paper is to provide a reliable tool to enclose these differential equations. Its use is s...