Brief Announcement: Cooperative Guarding in Polygons with Holes

We study the Cooperative Guarding problem for polygons with holes in a mobile multi-agents setting. Given a set of agents, initially deployed at a point in a polygon with n vertices and h holes, we require the agents to collaboratively explore and position themselves in such a way that every point in the polygon is visible to at least one agent and that the set of agents are visibly connected. We study the problem under two models of computation, one in which the agents can compute exact distances and angles between two points in its visibility, and one in which agents can only compare distances and angles. In the stronger model, we provide a deterministic O(n) round algorithm to compute such a cooperative guard set while not requiring more than (n + h)/2 agents and O(log n) bits of persistent memory per agent. In the weaker model, we provide an O(n?) round algorithm, that does not require more than (n+2h)/2 agents

Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes

This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of the environment, and operate only under line-of-sight sensing and communication. The objective of the deployment is for the agents to achieve full visibility coverage of the environment while maintaining line-of-sight connectivity with each other. This is achieved by incrementally partitioning the environment into distinct regions, each completely visible from some agent. Proofs are given of (i) convergence, (ii) upper bounds on the time and number of agents required, and (iii) bounds on the memory and communication complexity. Simulation results and description of robust extensions are also included

The Visibility Freeze-Tag Problem

In the Freeze-Tag Problem, we are given a set of robots at points inside some metric space. Initially, all the robots are frozen except one. That robot can awaken (or “unfreeze”) another robot by moving to its position, and once a robot is awakened, it can move and help to awaken other robots. The goal is to awaken all the robots in the shortest time. The Freeze-Tag Problem has been studied in different metric spaces: graphs and Euclidean spaces. In this thesis, we look at the Freeze-Tag Problem in polygons, and we introduce the Visibility Freeze-Tag Problem, where one robot can awaken another robot by “seeing” it. Furthermore, we introduce a variant of the Visibility Freeze-Tag Problem, called the Line/Point Freeze Tag Problem, where each robot lies on an awakening line, and one robot can awaken another robot by touching its awakening line. We survey the current results for the Freeze-Tag Problem in graphs, Euclidean spaces and polygons. Since the Visibility Freeze-Tag Problem bears some resemblance to the Watchman Route Problem, we also survey the background literature on the Watchman Route Problem. We show that the Freeze-Tag Problem in polygons and the Visibility Freeze-Tag Problem are NP-hard, and we present an O(n)-approximation algorithm for the Visibility Freeze-Tag Problem. For the Line/Point Freeze-Tag Problem, we give a polynomial time algorithm for the special case where all the awakening lines are parallel to each other. We prove that the general case is NP-hard, and we present an O(1)- approximation algorithm

Geometric optimization on visibility problems: metaheuristic and exact solutions

Doutoramento em MatemáticaOs problemas de visibilidade têm diversas aplicações a situações reais. Entre os mais conhecidos, e exaustivamente estudados, estão os que envolvem os conceitos de vigilância e ocultação em estruturas geométricas (problemas de vigilância e ocultação). Neste trabalho são estudados problemas de visibilidade em estruturas geométricas conhecidas como polígonos, uma vez que estes podem representar, de forma apropriada, muitos dos objectos reais e são de fácil manipulação computacional. O objectivo dos problemas de vigilância é a determinação do número mínimo de posições para a colocação de dispositivos num dado polígono, de modo a que estes dispositivos consigam “ver” a totalidade do polígono. Por outro lado, o objectivo dos problemas de ocultação é a determinação do número máximo de posições num dado polígono, de modo a que quaisquer duas posições não se consigam “ver”. Infelizmente, a maior parte dos problemas de visibilidade em polígonos são NP-difíceis, o que dá origem a duas linhas de investigação: o desenvolvimento de algoritmos que estabelecem soluções aproximadas e a determinação de soluções exactas para classes especiais de polígonos. Atendendo a estas duas linhas de investigação, o trabalho é dividido em duas partes. Na primeira parte são propostos algoritmos aproximados, baseados essencialmente em metaheurísticas e metaheurísticas híbridas, para resolver alguns problemas de visibilidade, tanto em polígonos arbitrários como ortogonais. Os problemas estudados são os seguintes: “Maximum Hidden Vertex Set problem”, “Minimum Vertex Guard Set problem”, “Minimum Vertex Floodlight Set problem” e “Minimum Vertex k-Modem Set problem”. São também desenvolvidos métodos que permitem determinar a razão de aproximação dos algoritmos propostos. Para cada problema são implementados os algoritmos apresentados e é realizado um estudo estatístico para estabelecer qual o algoritmo que obtém as melhores soluções num tempo razoável. Este estudo permite concluir que as metaheurísticas híbridas são, em geral, as melhores estratégias para resolver os problemas de visibilidade estudados. Na segunda parte desta dissertação são abordados os problemas “Minimum Vertex Guard Set”, “Maximum Hidden Set” e “Maximum Hidden Vertex Set”, onde são identificadas e estudadas algumas classes de polígonos para as quais são determinadas soluções exactas e/ou limites combinatórios.Visibility problems have several applications to real-life problems. Among the most distinguished and exhaustively studied visibility problems are the ones involving concepts of guarding and hiding on geometrical structures (guarding and hiding problems). This work deals with visibility problems on geometrical structures known as polygons, since polygons are appropriate representations of many real-world objects and are easily handled by computers. The objective of the guarding problems studied in this thesis is to find a minimum number of device positions on a given polygon such that these devices collectively ''see'' the whole polygon. On the other hand, the goal of the hiding problems is to find a maximum number of positions on a given polygon such that no two of these positions can “see" each other. Unfortunately, most of the visibility problems on polygons are NP-hard, which opens two lines of investigation: the development of algorithms that establish approximate solutions and the determination of exact solutions on special classes of polygons. Accordingly, this work is divided in two parts where these two lines of investigation are considered. The first part of this thesis proposes approximation algorithms, mainly based on metaheuristics and hybrid metaheuristics, to tackle some visibility problems on arbitrary and orthogonal polygons. The addressed problems are the Maximum Hidden Vertex Set problem, the Minimum Vertex Guard Set problem, the Minimum Vertex Floodlight Set problem and the Minimum Vertex k-Modem Set problem. Methods that allow the determination of the performance ratio of the developed algorithms are also proposed. For each problem, the proposed algorithms are implemented and a statistical study is performed to determine which of the developed methods obtains the best solution in a reasonable amount of time. This study allows to conclude that, in general, the hybrid metaheuristics are the best approach to solve the studied visibility problems. The second part of this dissertation addresses the Minimum Vertex Guard Set problem, the Maximum Hidden Set problem and the Maximum Hidden Vertex Set problem, where some classes of polygons are identified and studied and for which are determined exact solutions and/or combinatorial bounds

On realistic target coverage by autonomous drones

Low-cost mini-drones with advanced sensing and maneuverability enable a new class of intelligent sensing systems. To achieve the full potential of such drones, it is necessary to develop new enhanced formulations of both common and emerging sensing scenarios. Namely, several fundamental challenges in visual sensing are yet to be solved including (1) fitting sizable targets in camera frames; (2) positioning cameras at effective viewpoints matching target poses; and (3) accounting for occlusion by elements in the environment, including other targets. In this article, we introduce Argus, an autonomous system that utilizes drones to collect target information incrementally through a two-tier architecture. To tackle the stated challenges, Argus employs a novel geometric model that captures both target shapes and coverage constraints. Recognizing drones as the scarcest resource, Argus aims to minimize the number of drones required to cover a set of targets. We prove this problem is NP-hard, and even hard to approximate, before deriving a best-possible approximation algorithm along with a competitive sampling heuristic which runs up to 100× faster according to large-scale simulations. To test Argus in action, we demonstrate and analyze its performance on a prototype implementation. Finally, we present a number of extensions to accommodate more application requirements and highlight some open problems

Wide-Area Surveillance System using a UAV Helicopter Interceptor and Sensor Placement Planning Techniques

This project proposes and describes the implementation of a wide-area surveillance system comprised of a sensor/interceptor placement planning and an interceptor unmanned aerial vehicle (UAV) helicopter. Given the 2-D layout of an area, the planning system optimally places perimeter cameras based on maximum coverage and minimal cost. Part of this planning system includes the MATLAB implementation of Erdem and Sclaroff’s Radial Sweep algorithm for visibility polygon generation. Additionally, 2-D camera modeling is proposed for both fixed and PTZ cases. Finally, the interceptor is also placed to minimize shortest-path flight time to any point on the perimeter during a detection event. Secondly, a basic flight control system for the UAV helicopter is designed and implemented. The flight control system’s primary goal is to hover the helicopter in place when a human operator holds an automatic-flight switch. This system represents the first step in a complete waypoint-navigation flight control system. The flight control system is based on an inertial measurement unit (IMU) and a proportional-integral-derivative (PID) controller. This system is implemented using a general-purpose personal computer (GPPC) running Windows XP and other commercial off-the-shelf (COTS) hardware. This setup differs from other helicopter control systems which typically use custom embedded solutions or micro-controllers. Experiments demonstrate the sensor placement planning achieving \u3e90% coverage at optimized-cost for several typical areas given multiple camera types and parameters. Furthermore, the helicopter flight control system experiments achieve hovering success over short flight periods. However, the final conclusion is that the COTS IMU is insufficient for high-speed, high-frequency applications such as a helicopter control system

Geometría computacional y bases de datos espacio-temporales

Respecto de las temáticas de investigación, hemos vinculado las disciplinas Bases de Datos, Geometría Computacional y Metaheurísticas, debido a que en diversas aplicaciones dentro del campo de las Ciencias de la Computación se requiere la construcción y manejo de diferentes objetos geométricos, con propiedades deseables. También, se requiere de repositorios no tradicionales, que conllevan a nuevos modelos de bases de datos para administrar y buscar información en ellos. Así, surge la necesidad de estudiar modelos como las bases de datos espacio-temporales. En particular, algunos de los problemas estudiados necesitan algoritmos eficientes para su resolución, pero dada su naturaleza NP-dura, utilizamos técnicas metaheurísticas para hallar soluciones aproximadas. En este trabajo, presentamos los tópicos más relevantes, actualmente en estudio, con las propuestas más recientes y/o de interés.Eje: Ingeniería de Software y Base de DatosRed de Universidades con Carreras en Informática (RedUNCI

Geometría computacional y bases de datos espacio-temporales

Respecto de las temáticas de investigación, hemos vinculado las disciplinas Bases de Datos, Geometría Computacional y Metaheurísticas, debido a que en diversas aplicaciones dentro del campo de las Ciencias de la Computación se requiere la construcción y manejo de diferentes objetos geométricos, con propiedades deseables. También, se requiere de repositorios no tradicionales, que conllevan a nuevos modelos de bases de datos para administrar y buscar información en ellos. Así, surge la necesidad de estudiar modelos como las bases de datos espacio-temporales. En particular, algunos de los problemas estudiados necesitan algoritmos eficientes para su resolución, pero dada su naturaleza NP-dura, utilizamos técnicas metaheurísticas para hallar soluciones aproximadas. En este trabajo, presentamos los tópicos más relevantes, actualmente en estudio, con las propuestas más recientes y/o de interés.Eje: Ingeniería de Software y Base de DatosRed de Universidades con Carreras en Informática (RedUNCI