Coverage problems are quite old in the literature of various settings and disciplines. For instance, the famous art gallery problem was posed in 1973, in the context of computational geometry, and can be described as finding the minimum number of guards to supervise a gallery such that no point in the gallery is unwatched. Most of those problems were posed in a setting where a centralized decision maker (controller) could make decisions about the positioning and the number of guarding/sensing elements.

The proliferation of wireless sensors and the advances in miniaturization technology have made possible the construction of various sensors, some with the ability to sense physical quantities from the environment (for example, humidity, temperature, and pressure), others with cameras that can continuously monitor the environments, and so on. This technological explosion made the kind of problems related to terrain coverage by static or mobile sensors, which also form a wireless ad hoc network, blossom [1]. So, problems related to perimeter coverage, barrier coverage, target tracking, and many others, with static or mobile sensors, with deterministic or probabilistic sensing models, with omnidirectional or directional antennae in 2D/3D wireless networks, have been studied, usually under connectivity constraints. Most of these works focus on the algorithmic and engineering aspects of these problems, and to a large degree ignore mathematical analysis of the developed solutions. In the wireless sensor network setting, any solution to a coverage problem must be distributed, that is, to be based on cooperation among the sensors and limited knowledge of the network topology or of the environment. These constraints make the development of a solution for coverage problems much more difficult than in a centralized setting.

This book, written by prominent researchers and educators, targets the kind of coverage problems that involve mobile sensors and actuators and that admit a distributed solution; its main target area is robotics. In its ten chapters, it describes distributed solutions for barrier and blanket coverage problems under various settings, paying special attention and emphasis to their proven analytic performance, but providing also experimental (simulated) results.

The main audience of the book is advanced undergraduate or graduate students, as well as professionals (engineers or mathematicians), researchers, and developers who insist on obtaining a broad knowledge and deep understanding of a particular matter. Even though it cannot be used as a textbook because it lacks exercises, the wealth of figures and illustrations offer additional insights into the studied topics. Overall, it is a welcome book in the coverage problems literature.