# Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

Francesco Bullo
Jorge Cortés
Sonia Martínez
Pages: 336
https://www.jstor.org/stable/j.ctt7rr4k

1. Front Matter
(pp. i-vi)
(pp. vii-viii)
3. Preface
(pp. ix-xii)
Francesco Bullo, Jorge Cortés and Sonia Martínez
4. Chapter One An introduction to distributed algorithms
(pp. 1-94)

Graph theory, distributed algorithms, and linear distributed algorithms are a fascinating scientific subject. In this chapter we provide a broad introduction to distributed algorithms by reviewing some preliminary graphical concepts and by studying some simple algorithms. We begin the chapter with one section introducing some basic notation and another section stating a few useful facts from matrix theory, dynamical systems, and convergence theorems based on invariance principles. In the third section of the chapter, we provide a primer on graph theory with a particular emphasis on algebraic aspects, such as the properties of adjacency and Laplacian matrices associated to a...

5. Chapter Two Geometric models and optimization
(pp. 95-138)

This chapter presents various geometric objects and geometric optimization problems that have strong connections with motion coordination. Basic geometric notions such as polytopes, centers, partitions, and distances are ubiquitous in cooperative strategies, coordination tasks, and the interaction of robotic networks with the physical environment. The notion of Voronoi partition finds application in diverse areas such as wireless communications, signal compression, facility location, and mesh optimization. Proximity graphs provide a natural way to mathematically model the network interconnection topology resulting from the agents’ sensing and/or communication capabilities. Finally, multicenter functions play the role of aggregate objective functions in geometric optimization problems....

6. Chapter Three Robotic network models and complexity notions
(pp. 139-178)

This chapter introduces the main subject of study of this book, namely a model for groups of robots that sense their own position, exchange messages according to a geometric communication topology, process information, and control their motion. We refer to such systems as robotic networks. The content of this chapter has evolved from Martínez et al. (2007a).

The chapter is organized as follows. The first section contains the formal model. We begin by presenting the physical components of a network, that is, the mobile robots and the communication service connecting them. We then present the notion of control and communication...

7. Chapter Four Connectivity maintenance and rendezvous
(pp. 179-218)

The aims of this chapter are twofold. First, we introduce the rendezvous problem and analyze various coordination algorithms that achieve it, providing upper and lower bounds on their time complexity. Second, we introduce the problem of maintaining connectivity among a group of mobile robots and use geometric approaches to preserve this topological property of the network.

Loosely speaking, therendezvous objectiveis to achieve agreement over the physical location of as many robots as possible, that is, to steer the robots to a common location. This objective is to be achieved with the limited information flow described in the model...

8. Chapter Five Deployment
(pp. 219-246)

The aim of this chapter is to present various solutions to the deployment problem. Thedeployment objectiveis to optimally place a group of robots in an environment of interest. The approach taken here consists of identifying aggregate functions that measure the quality of deployment of a given network configuration and designing control and communication laws that optimize these measures.

The variety of algorithms presented in the chapter stems from two causes. First, different solutions arise from the interplay between the spatially distributed character of the coordination algorithms and the limited sensing and communication capabilities of the robotic network. As...

9. Chapter Six Boundary estimation and tracking
(pp. 247-278)

The aim of this chapter is to provide an example of a motion coordination algorithm that can be used in a specific sensing task. This is the task of detection and estimation of an evolving boundary in two dimensions by a robotic sensor network. This type of operation can be of interest in the validation of oceanographic and atmospheric models, as well as for the demarcation of hazardous environments. In the ocean, a boundary can delimit areas where there are abrupt changes in temperature, which can influence the marine biodiversity in those areas. In the atmosphere, a boundary can establish...

10. Bibliography
(pp. 279-304)
11. Algorithm Index
(pp. 305-306)
12. Subject Index
(pp. 307-312)
13. Symbol Index
(pp. 313-320)