Localization for underwater robots remains a challenging issue. Typical 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 Simultaneous Localization and Mapping (SLAM) methods to perform localization. Reliable Robot Localization presents an innovative new method which can be characterized as a raw-data SLAM approach. It differs from extant methods by considering time as a standard variable to be estimated, thus raising new opportunities for state estimation, so far underexploited. However, such temporal resolution is not straightforward and requires a set of theoretical tools in order to achieve the main purpose of localization. This book not only presents original contributions to the field of mobile robotics, it also offers new perspectives on constraint programming and set-membership approaches. It provides a reliable contractor programming framework in order to build solvers for dynamical systems. This set of tools is illustrated throughout this book with realistic robotic applications.

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Information

Publisher

Wiley-ISTE

Year

2019

ISBN

9781119680963

Edition

Topic

Technology & Engineering

Subtopic

Robotics

Index

Technology & Engineering

PART 1
Interval Tools

Introduction to Part 1

We aim to address robotics problems with set-membership methods. In this part, we introduce a set of already existing tools based on interval analysis, illustrated using several simple examples of dead-reckoning and range-only state estimation. Each notion developed in this part will then be applied in the following chapters.

Chapter 1 introduces the concepts of interval analysis, constraint programming, contractors and set-inversion. Chapter 2 extends the approach to temporal systems by providing the notion of tubes with their related properties, algebraic contractors and implementation choices.

1
Static Set-membership State Estimation

1.1. Introduction

A state estimation problem can be dealt with by set-membership approaches, where both the uncertainties on the model and the measurements errors are known. By known, we mean that an unknown actual value is guaranteed to lie within bounds that delineate the uncertainties, thus defining a solution set (Walter and Piet-Lahanier 1988, Cerone 1996, Veres and Norton 1996, Maksarov and Norton 1996).

The estimation then consists of reducing this set of feasible values by means of operators, where other approaches would have minimized an error criterion. The computations are not performed in a probabilistic way but based on deterministic operations on the bounds of the set. This approach is significantly different from usual methods: here, we do not assume a probability distribution in the calculations. Furthermore, the bounding property of such an approach is guaranteed even though the system is nonlinear. This quality is of particular importance in mobile robotics where several problems present nonlinearities, the case of a range-only localization being one of them (Caiti et al. 2005).

Range-only state estimation

A telling example of set-membership state estimation is the localization of a mobile robot among beacons. This kind of application has already been appropriately presented in Drevelle (2011) to introduce set-membership methods. We will use it as a guiding thread of this book, first in this chapter in a static context without considering temporal evolutions: the pose of the robot is estimated with synchronous measurements. The same example will be extended to dynamical state estimation in Chapters 2, 3 and 4 based on differential st...

Cover
Table of Contents
Preface
Notations
Abbreviations
Introduction
PART 1: Interval Tools
PART 2: Constraints-related Contributions
PART 3: Robotics-related Contributions
Conclusion
References
Index
End User License Agreement