The book provides a unified and systematic view of the authors’ research in the area of swarm robotics, with an emphasis on swarm applications for search missions. A lot of the included work is previously published material. The book focuses on mathematical tools useful to the design and analysis of swarm systems. Information about such tools is often lacking, so the book is a welcome addition.

The book can be divided into three sections. The first (and by far the largest) section is on swarms of robots searching on a grid to do cooperative cleaning. Robots communicate only indirectly through pheromones. The material covered goes from static environments with no obstacles, to environments with obstacles, to dynamic environments where some of the cleaned area needs to be cleaned again because of recontamination. The second section looks at swarm systems in stochastic environments, where the area and size of the area to be cleaned are unknown and grow with some probability at every time step. The third section is on using unmanned aerial vehicles (UAVs) to search efficiently for a group of evading targets. Here the problem becomes a hunting problem. The book ends with a patrolling problem, which is addressed as an optimization problem (that is, to optimize the number and types of drones) and with a case study on monitoring a real large-scale transportation network.

The material is presented in a mathematically rigorous way, providing algorithms, bounds on complexity, theorems, and impossibility theorems. In addition to the theoretical results, the book also includes some experimental results. Overall, the book is a solid attempt to formally characterize the properties of domains and the swarms of robots operating in them. The algorithms are often described with figures that show sample environments and how the operations progress over time. This provides a good understanding of how the algorithms work. Graphs are used to illustrate the effects of choosing different parameters or of contaminated regions of different shapes.

A limitation of the material presented is the fact that the search regions are always assumed to be planar and represented as a grid. The 2D assumption limits the ability of drones to cover nonflat areas and to fly at different altitudes. The fact that all the methods presented are based on geometry limits the choice of methods in the hunting and patrolling problems, where some game-theoretic approaches would have been interesting. Of course, it is impossible to cover in one book all the different approaches. Each chapter has its own set of references, which is nice; however, it does make it hard to see the entire set of works cited. Many papers are cited in multiple chapters, so the references are repeated. Overall, the limitations do not detract from the book’s value for anyone who is serious about studying swarm robotics with mathematical and algorithmic methods.