Probabilistic Bases

This is the third chapter of the first section. It is a compendium of all the concepts and theorems of probability theory that are found in the problems of Bayesian estimation of a robot location and the map of its environment. It presents uncertainty as an intrinsic feature of any mobile robot that develops in a real environment. It is then discussed how uncertainty has been treated along the history of science and how probabilistic approaches have represented such a huge success in many engineering fields, including robotics. The fundamental concepts of probability theory are discussed along with some advanced topics needed in further chapters, following a learning curve as smooth and comprehensive as possible.

The Bayesian Approach to SLAM

This is the second chapter of the third section. It deals with the situation arising when neither the environment nor the exact localization of a mobile robot are known, that is, when we face the hard problem of SLAM. It reviews the most common solutions to that problem found in literature, especially those based on statistical estimation. Both parametric and non-parametric filters are explained as practical solutions to this problem, including analysis of their advantages and weaknesses that must be both taken into account in order to design a robust SLAM system. Complete examples and algorithms for these filters are included.

Mobile Robot Localization with Recursive Bayesian Filters

In this last chapter of the second section, the authors present probabilistic solutions to mobile robot localization that bring together the recursive filters introduced in chapter 4 and all the components and models already discussed in the preceding chapters. It presents the general, Bayesian framework for a probabilistic solution to localization and mapping. The problem is formally described as a graphical model (in particular a dynamic Bayesian network), and the characteristics that can be exploited to approach it efficiently are elaborated. Among parametric Bayesian estimators, the family of the Kalman filters is introduced with examples and practical applications. Then, the more modern non-parametric filters, mainly particle filters, are explained. Due to the diversity of filters available for localization, comparative tables are included.

Robot Motion Models

This is the first chapter of the second section, a section devoted to mobile robot localization. Before presenting the general Bayesian framework for that problem at chapter 7, it is first required to study the different probabilistic models of robot motion. This chapter explores some of the reasons why any real robot cannot move as perfectly as planned, thus demanding a probabilistic model of the robot actions—mainly, its movements. Special emphasis is put on the most common ground wheeled robots, although other configurations (including non-robotic ones) with more degrees of freedom, such as arbitrarily-moving hand-held sensors or aerial vehicles, are also mentioned. The best-known approximate probabilistic models for robot motion are provided and justified.

Robotic Bases

This is the second chapter of the first section. It presents the mechanical and physical foundations of mobile robots that are needed for a complete understanding of the concepts of further chapters, such as sensor and motion models. It provides a detailed review of the most common electro-mechanical components found in state-of-the-art mobile robots, emphasizing practical aspects, such as weight and size, power consumption, and performance trade-offs. Sensors and actuators, in particular, are stated as the hardware basis for coping with localization and mapping, and thus, specialized sections are devoted to them. The described devices range from low-cost sensors/actuators suitable for hobbyists to expensive professional-grade components.

Maps for Mobile Robots

This is the first chapter of the third section. It describes the kinds of mathematical models usable by a mobile robot to represent its spatial reality, and the reasons by which some of them are more useful than others, depending on the task to be carried out. The most common metric, topological, and hybrid map representations are described from an introductory viewpoint, emphasizing their limitations and advantages for the localization and mapping problems. It then addresses the problem of how to update or build a map from the robot raw sensory data, assuming known robot positions, a situation that becomes an intrinsic feature of some SLAM filters. Since the process greatly depends on the kind of map and sensors, the most common combinations of both are shown.

Sensor Models

This is the second chapter of the second section. Analogously to chapter 5, here the authors study probabilistic models of sensors, which is the second fundamental component of the general Bayesian framework for localization. In this chapter, they explain common mathematical models of sensors, stressing their differences and effects in further estimation techniques, in particular whether they are parametrical or not. The chapter also points out the existence of the association problem between observations and known elements of maps for some kinds of sensors, and presents solutions to that problem. Finally, some methods for matching local maps provided by particular kinds of sensors are also included.

Advanced SLAM Techniques

This chapter is the conclusion of the book. It is devoted to providing an overview of emerging paradigms that are appearing as outstanding the traditional approaches in scalability or efficiency, such as hierarchical sub-mapping, or hybrid metric-topological map models. Other techniques not based on Bayesian filtering, such as iterative sparse least-squares optimization (Graph-SLAM and Bundle adjustment), are also introduced due to their efficiency and increasing popularity.

Statistical Bases

This is the fourth and last chapter of the first section. As chapter 3 introduced the mathematical tools of probability theory needed to understand all the concepts in the book, chapter 4 does the same concerning statistics. It fills the gap between probability theory and real data coming from stochastic processes, highlighting the great amount of potential applications of the different fields of statistics—particularly estimation theory—in state-of-the-art science and engineering. Topics covered in this chapter include the fundamental tools needed in probabilistic robotics: probabilistic convergence, theory of estimators, hypothesis tests, etc. Special stress is on recursive Bayesian estimators, due to their central role in the problems of probabilistic robot localization and mapping.

Introduction

In this first chapter of the book, the authors provide an overview of the problems of mobile robot localization and mapping, including taxonomies over the axes of the representation of spatial knowledge, the structure and dynamics of the environment, the sensory apparatus of the robot, the motor apparatus of the robot, and the previous knowledge. They also provide a brief historical timeline and fundamental concepts. The goal is to provide the reader with a roadmap of the problems and also of the book, in order to allow her or him to choose the best way of approaching the text and also an appropriate understanding of the main limitations of the existing methods.