Robots with Lights: Overcoming Obstructed Visibility Without Colliding

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation of computability in this model, initially suggested by Peleg, is under way, and several results have been recently established. In these investigations, however, an agent is assumed to be capable to see through another agent. In this paper we start the study of computing when visibility is obstructable, and investigate the most basic problem for this setting, Complete Visibility: The agents must reach within finite time a configuration where they can all see each other and terminate. We do not make any assumption on a-priori knowledge of the number of agents, on rigidity of movements nor on chirality. The local coordinate system of an agent may change at each activation. Also, by definition of lights, an agent can communicate and remember only a constant number of bits in each cycle. In spite of these weak conditions, we prove that Complete Visibility is always solvable, even in the asynchronous setting, without collisions and using a small constant number of colors. The proof is constructive. We also show how to extend our protocol for Complete Visibility so that, with the same number of colors, the agents solve the (non-uniform) Circle Formation problem with obstructed visibility

Pattern formation

The Pattern Formation problem is one of the most important coordination problem for robotic systems. Initially the entities are in arbitrary positions; within finite time they must arrange themselves in the space so to form a pattern given in input. In this chapter, we will mainly deal with the problem in the OBLOT model

The Firework Book: An edition, translation, and analysis of Royal Armouries Ms. I.34 as an example of tradition and change in fifteenth‐century gunpowder technology

In the Royal Armouries collection is a manuscript which comprises a text in Early New High German, known as RA I.34. It has never been published in its entirety, and has never been transcribed or translated. It forms part of a corpus of Firework Books which were produced from the early fifteenth century onwards. In total, 65 fragments of the Firework Book could be traced, and each text has different content and components while retaining core elements of text common to all. The Firework Book is a significant example of the development of fifteenth‐century gunpowder technology and makes a core contribution to arguments surrounding the so‐called ‘Military Revolution’. RA I.34 displays common core elements of the Firework Book tradition, but it is also distinctive in a number of different ways. Unlike most copies of the Firework Book RA I.34 is still in what appears to be its original format and binding, with text written by two distinctly different hands with regional variations in the language. It also contains a section with illustrations. This thesis provides an edition and translation into English of RA I.34, an analysis of its content, and a comparison to other Firework Book manuscripts, and their historiography. Chapter 1 provides a description of the Firework Book tradition and its historiography. Chapter 2 provides a description of the physical attributes, the content and the provenance of RA I.34. Chapter 3 comprises an edition of the manuscript and a translation from Early New High German into English. Chapter 4 offers a close analysis of the content of the text of RA I.34 while chapter 5 explores the use and the ownership of the Firework Book. This thesis positions the Firework Book at a crucial stage in the development of gunpowder artillery, thus offering an unparalleled insight into fifteenth‐century gunpowder technology, and its position in the change of military technology at the end of the Middle Ages

Self-deployment Algorithms for Mobile Sensors on a Ring

We consider the self-deployment problem in a ring for a network of identical sensors: starting from some initial random placement in the ring, the sensors in the network must move, in a purely decentralized and distributed fashion, so to reach in finite time a state of static equilibrium in which they evenly cover the ring. A self-deployment algorithm is exact if within finite time the sensors reach a static uniform configuration: the distance between any two consecutive sensors along the ring is the same, d; the self-deployment algorithm is ɛ-approximate if the distance between two consecutive sensors is between d − ɛ and d + ɛ. We prove that exact self-deployment is impossible if the sensors do not share a common orientation of the ring. We then consider the problem in an oriented ring. We prove that if the sensors know the desired final distance d, thenexact self-deployment is possible. Otherwise, we present another protocol based on a very simple strategy and prove that it is ɛ-approximate for any chosen ɛ>0. Our results show that a shared orientation of the ring is an important computational and complexity factor for a network of mobile sensors operating in a ring

Getting Close Without Touching

In this paper we study the Near-Gathering problem for a set of asynchronous, anonymous, oblivious and autonomous mobile robots with limited visibility moving in Look-Compute-Move (LCM) cycles: In this problem, the robots have to get close enough to each other, so that every robot can see all the others, without touching (i.e., colliding) with any other robot. The importance of this problem might not be clear at a first sight: Solving the Near-Gathering problem, it is possible to overcome the limitations of having robots with limited visibility, and it is therefore possible to exploit all the studies (the majority, actually) done on this topic, in the unlimited visibility setting. In fact, after the robots get close enough, they are able to see all the robots in the system, a scenario similar to the one where the robots have unlimited visibility. Here, we present a collision-free algorithm for the Near-Gathering problem, the first to our knowledge, that allows a set of autonomous mobile robots to nearly gather within finite time. The collision-free feature of our solution is crucial in order to combine it with an unlimited visibility protocol. In fact, the majority of the algorithms that can be found on the topic assume that all robots occupy distinct positions at the beginning. Hence, only providing a collision-free Near-Gathering algorithm, as the one presented here, is it possible to successfully combine it with an unlimited visibility protocol, hence overcoming the natural limitations of the limited visibility scenario. In our model, distances are induced by the infinity norm. A discussion on how to extend our algorithm to models with different distance functions, including the usual Euclidean distance, is also presented