Distributed Control of Robotic Networks By Francesco Bullo Jorge Cort´es Sonia Mart´ınez
Recent years have witnessed a thriving research activity on cooperative control and motion coordination. This interest is motivated by the growing possibilities enabled by robotic networks in the monitoring of natural phenomena and the enhancement of human capabilities in hazardous and unknown environments.
Our first objective in this book is to present a coherent introduction to basic distributed algorithms for robotic networks. This emerging discipline sits at the intersection of different areas such as distributed algorithms, parallel processing, control, and estimation. Our second objective is to provide a self-contained, broad exposition of the notions and tools from these areas that are relevant in cooperative control problems. These concepts include graph-theoretic notions (connectivity, adjacency, and Laplacian matrices), distributed algorithms from computer science (leader election, basic tree computations) and from parallel processing (averaging algorithms, convergence rates), and geometric models and optimization (Voronoi partitions, proximity graphs). Our third objective is to put forth a model for robotic networks that helps to rigorously formalize coordination algorithms running on them. We illustrate how computational geometry plays an important role in modeling the interconnection topology of robotic networks. We draw on classical notions from distributed algorithms to provide complexity measures that characterize the execution of coordination algorithms. Such measures allow us to quantify the algorithm performance and implementation costs. Our fourth and last objective is to present various algorithms for coordination tasks such as connectivity maintenance, rendezvous, and deployment. We especially emphasize the analysis of the correctness and of the complexity of the proposed algorithms. The technical treatment combines controltheoretic tools such as Lyapunov functions and invariance principles with techniques from computer science and parallel processing, such as induction and message counting.
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