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## Über dieses Buch

This book offers a comprehensive analysis of the theory and tools needed for the development of an efficient and robust infrastructure for the design of collaborative patrolling unmanned aerial vehicle (UAV) swarms, focusing on its applications for tactical intelligence drones. It discusses frameworks for robustly and near-optimally analyzing flocks of semi-autonomous vehicles designed to efficiently perform the ongoing dynamic patrolling and scanning of pre-defined “search regions”. It discusses the theoretical limitations of such systems, as well as the trade-offs between the systems’ various economic and operational parameters.
Current UAV systems rely mainly on human operators for the design and adaptation of drones’ flying routes. However, recent technological advances have introduced new systems, comprised of a small number of self-organizing vehicles, manually guided at the swarm level by a human operator.
With the growing complexity of such man-supervised architectures, it is becoming increasingly harder to guarantee a pre-defined level of performance. The use of large scale swarms of UAVs as a combat and reconnaissance platform therefore necessitates the development of an efficient optimization mechanism of their utilization, specifically in the design and maintenance of their patrolling routes.
The book is intended for researchers and engineers in the fields of swarms systems and autonomous drones.

## Inhaltsverzeichnis

### Introduction to Swarm Search

This book aims to bring to the forefront innovative approaches for the design and analysis of Swarm Search systems and methodologies. Specifically, the book offers a comprehensive analysis of the theory and tools needed for the development of an efficient and robust infrastructure for the design of collaborative patrolling UAV swarms, focusing on its applications for tactic intelligence drones. This Introduction shortly reviews the analysis scope of the book, as well as provides a short summary of each of its chapters.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### Cooperative “Swarm Cleaning” of Stationary Domains

In this work we analyze the behavior of a swarm of autonomous robotic agents, or drones, designed for cooperatively exploring an unknown area (for purposes of cleaning, painting, etc.). We assume that each robot can acquire only the information which is available in its immediate vicinity, and the only way of inter-robot communication is by leaving traces on the common ground and sensing the traces left by other robots. We present a protocol for cleaning a dirty area that guarantees task completion (unless all robots die) and prove an upper bound on the time complexity of this protocol. We also show simulation results of the protocol on several types of regions. These simulations indicate that the precise cleaning time depends on the number of robots, their initial locations, and the shape of the dirty region.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### Swarm Search of Expanding Regions in Grids: Lower Bounds

In this chapter we examine the dynamic generalization of the Cooperative Cleaners problem presented in [10] and in the previous chapter of this book, involving a swarm of collaborative drones that are required to search a dynamically expanding region on the $$\mathbf {Z}^{2}$$ grid (whose “pixels” that were visited by the drones can become “un-searched” after a certain period of time). The goal of the swarm’s members is to “clean” the spreading contamination in as little time as possible. In this work we present an algorithm-agnostic lower bound for the problem, as well as a collaborative swarm search algorithm, accompanied with a variety of experimental results.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### Swarm Search of Expanding Regions in Grids: Upper Bounds

In this chapter we examine the dynamic generalization of the Cooperative Cleaners problem presented in Altshuler et al., Swarm intelligent systems (2006), [10] and in the previous chapters of this book, involving a swarm of collaborative drones that are required to search a dynamically expanding region on the $$\mathbf{Z}^{2}$$ grid (whose “pixels” that were visited by the drones can become “un-searched” after a certain period of time). The goal of the swarm’s members is to “clean” the spreading contamination in as little time as possible. In this work we present a collaborative swarm search algorithm, as well as several upper bounds on the completion time it takes a swarm of k drones, of various velocities.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### The Search Complexity of Collaborative Swarms in Expanding Grid Regions

In this paper we study the strengths and limitations of collaborative swarms of simple agents. In particular, we discuss the efficient use of simple drones, or “ant robots” for covering a connected region on the $$\mathbf{Z}^{2}$$ grid, whose area is unknown in advance, and which expands at a given rate, where n is the initial size of the connected region. We show that regardless of the algorithm used, and the robots’ hardware and software specifications, the minimal number of robots required in order for such coverage to be possible is $$\varOmega ({\sqrt{n}})$$. In addition, we show that when the region expands at a sufficiently slow rate, a team of $$\varTheta (\sqrt{n})$$ robots could cover it in at most $$O(n^{2} \ln n)$$ time. This completion time can even be achieved by myopic robots, with no ability to directly communicate with each other, and where each robot is equipped with a memory of size O(1) bits w.r.t the size of the region (therefore, the robots cannot maintain maps of the terrain, nor plan complete paths). Regarding the coverage of non-expanding regions in the grid, we improve the current best known result of $$O(n^{2})$$ by demonstrating an algorithm that guarantees such a coverage with completion time of $$O(\frac{1}{k} n^{1.5} + n)$$ in the worst case, and faster for shapes of perimeter length which is shorter than O(n).
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### Collaborative Patrolling Swarms in Stochastically Expanding Environments

In this work we study the strengths and limitations of collaborative teams of simple robotic agents, operating in stochastic environments. In particular, we discuss the efficient use of a swarm of “ant robots” (e.h. simple drones with a limited technical specifications) for covering a connected region on the $$\mathbf{Z}^{2}$$ grid, whose area and shape is unknown in advance and which expands stochastically. Specifically, we discuss the problem where an initial connected region of $$S_0$$ “squares” expands outward with probability p at every time step. On this grid region a group of k limited and simple drone-agents operate, with the goal of “cleaning” this unmapped and dynamically expanding region. A preliminary version of this problem was discussed in [3, 7], involving a deterministic expansion of a region in the grid. We present probabilistic lower bounds for the minimal number of agents and minimal time required to enable a collaborative coverage of the expanding region, regardless of the algorithm used and the drones’ hardware and software specifications. Furthermore, we provide a method of producing ad-hoc lower bounds, for any given desired correctness probability. We further present impossibility results that for any given values of k (the number of drones used) and spreading probability provides an upper bound for the minimal value of the initial area of the expanding region which is guaranteed to be impossible to clear. Finally, we support the analytic bounds with empirical computer simulation results.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### The Cooperative Hunters – Efficient and Scalable Drones Swarm for Multiple Targets Detection

This work examines the Cooperative Hunters problem, where a swarm of Unmanned Air Vehicles (UAVs) is used for searching after one or more “evading targets”, which freely maneuver in a predefined area while trying to avoid detection by the swarm’s drones. By arranging themselves into an efficient geometric collaborative flight formation, the drones optimize their integrated sensing capabilities, enabling the completion of a successful search of a rectangular territory. This designed is shown to be able to guarantee the detection of the targets, even in cases where the targets are faster than the swarm’s drones and have better sensors. This is achieved through the inherent scalability of the proposed design which can compensate any addition to the targets’ ability to maneuver or foresee the behavior of the drones with an increase in the number of drones.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein

### Optimal Dynamic Coverage Infrastructure for Large-Scale Fleets of Reconnaissance UAVs

Current state of the art in the field of UAV activation relies solely on human operators for the design and adaptation of the drones flying routes. Furthermore, this is being done today on an individual level (one vehicle per operators), with some exceptions of a handful of new systems, that are comprised of a small number of self-organizing swarms, manually guided by a human operator. Drones-based monitoring is of great importance in variety of civilian domains, such as road safety, homeland security, and even environmental control. In its military aspect, efficiently detecting evading targets by a fleet of unmanned drones has an ever increasing impact on the ability of modern armies to engage in warfare. The latter is true both traditional symmetric conflicts among armies as well as asymmetric ones. Be it a speeding driver, a polluting trailer or a covert convoy, the basic challenge remains the same — how can its detection probability be maximized using as little number of drones as possible. In this work we propose a novel approach for the optimization of large scale swarms of reconnaissance drones — capable of producing on-demand optimal coverage strategies for any given search scenario. Given an estimation cost of the threat’s potential damages, as well as types of monitoring drones available and their comparative performance, our proposed method generates an analytically provable strategy, stating the optimal number and types of drones to be deployed, in order to cost-efficiently monitor a pre-defined region for targets maneuvering using a given roads networks. We demonstrate our model using a unique dataset of the Israeli transportation network, on which different deployment schemes for drones deployment are evaluated.
Yaniv Altshuler, Alex Pentland, Alfred M. Bruckstein
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