Benoît Desrochers

Set-membership approach to the kidnapped robot problem

This article depicts an algorithm which matches the output of a Lidar with an initial terrain model to estimate the absolute pose of a robot. Initial models do not perfectly fit the reality and the acquired data set can contain an unknown, and potentially large, proportion of outliers. We present an interval based algorithm that copes with such conditions, by matching the Lidar data with the terrain model in a robust manner. Experimental validations using different terrain model are reported to illustrate the performance of the method.

A minimal contractor for the polar equation

Contractor programming relies on a catalog on elementary contractors which need to be as efficient as possible. In this paper, we introduce a new theorem that can be used to build minimal contractors consistent with equations, and another new theorem to derive an optimal separator from a minimal contractor. As an application, we focus on the channeling polar constraint associated to the change between Cartesian coordinates and Polar coordinates. We illustrate our method on the localization problem of an actual underwater robot where both range and goniometric measurements of landmarks are collected.

Inner and Outer Approximations of Probabilistic Sets

This paper proposes a set-membership method to characterize a probabilistic set , i.e., a set enclosing the true value for the parameter vector of a parametric system with a given probability. The approach assumes that all errors are independent and an interval for the error is known. To each error interval, a probability to be an outlier is provided. It is shown that characterizing the probabilistic set is a set inversion problem. The main contribution of the paper is to provide a method to characterize the inner part of the probabilistic set. As an illustration, an application to the static localization of a mobile robot is considered.

Introduction to the Algebra of Separators with Application to Path Planning

Abstract Contractor algebra is a numerical tool based on interval analysis which makes it possible to solve many nonlinear problems arising in robotics, such as identification, path planning or robust control. This paper presents a new notion of separators which is a pair of complementary contractors and presents the corresponding algebra. Using separator algebra inside a paver will allow us to get an inner and an outer approximation of the solution set in a much simpler way than using any other interval approach. A path planning problem will then be considered in order to illustrate the principle of the approach.

Computing a Guaranteed Approximation of the Zone Explored by a Robot

This technical note deals with the guaranteed characterization of the part of the space that has been explored by a robot. The main difficulty of the problem is to take into account the uncertainty associated with the trajectory and the fact that the dimension of the visible space at time t may be smaller than that of the workspace. An example involving an experiment made with an actual underwater robot is presented in order to illustrate the efficiency of the approach.

Minkowski operations of sets with application to robot localization

This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.

Thick set inversion

Abstract This paper deals with the set inversion problem X = f − 1 ( Y ) in the case where the function f : R n → R m and the set Y are both uncertain. The uncertainty is treated under the form of intervals. More precisely, for all x, f ( x ) is inside the box [ f ] ( x ) and the uncertain set Y is bracketed between an inner set Y ⊂ and an outer set Y ⊃ . The introduction of new tools such as thick intervals and thick boxes will allow us to propose an efficient algorithm that handles the uncertainty of sets in an elegant and efficient manner. Some elementary test-cases that cannot be handled easily and properly by existing methods show the efficiency of the approach.