Competitive location problems : balanced facility location and the One-Round Manhattan Voronoi Game

We study competitive location problems in a continuous setting, in which facilities have to be placed in a rectangular domain R of normalized dimensions of 1 and ρ≥ 1 , and distances are measured according to the Manhattan metric. We show that the family of balanced facility configurations (in which the Voronoi cells of individual facilities are equalized with respect to a number of geometric properties) is considerably richer in this metric than for Euclidean distances. Our main result considers the One-Round Voronoi Game with Manhattan distances, in which first player White and then player Black each place n points in R; each player scores the area for which one of its facilities is closer than the facilities of the opponent. We give a tight characterization: White has a winning strategy if and only if ρ≥ n; for all other cases, we present a winning strategy for Black

Competitive location problems : balanced facility location and the one-round Manhattan Voronoi game

We study competitive location problems in a continuous setting, in which facilities have to be placed in a rectangular domain R of normalized dimensions of 1 and ρ≥1, and distances are measured according to the Manhattan metric. We show that the family of 'balanced' facility configurations (in which the Voronoi cells of individual facilities are equalized with respect to a number of geometric properties) is considerably richer in this metric than for Euclidean distances. Our main result considers the 'One-Round Voronoi Game' with Manhattan distances, in which first player White and then player Black each place n points in R; each player scores the area for which one of its facilities is closer than the facilities of the opponent. We give a tight characterization: White has a winning strategy if and only if ρ≥n; for all other cases, we present a winning strategy for Black

New Geometric Data Structures for Collision Detection

We present new geometric data structures for collision detection and more, including: Inner Sphere Trees - the first data structure to compute the peneration volume efficiently. Protosphere - an new algorithm to compute space filling sphere packings for arbitrary objects. Kinetic AABBs - a bounding volume hierarchy that is optimal in the number of updates when the objects deform. Kinetic Separation-List - an algorithm that is able to perform continuous collision detection for complex deformable objects in real-time. Moreover, we present applications of these new approaches to hand animation, real-time collision avoidance in dynamic environments for robots and haptic rendering, including a user study that exploits the influence of the degrees of freedom in complex haptic interactions. Last but not least, we present a new benchmarking suite for both, peformance and quality benchmarks, and a theoretic analysis of the running-time of bounding volume-based collision detection algorithms

Abstracting Multidimensional Concepts for Multilevel Decision Making in Multirobot Systems

Multirobot control architectures often require robotic tasks to be well defined before allocation. In complex missions, it is often difficult to decompose an objective into a set of well defined tasks; human operators generate a simplified representation based on experience and estimation. The result is a set of robot roles, which are not best suited to accomplishing those objectives. This thesis presents an alternative approach to generating multirobot control algorithms using task abstraction. By carefully analysing data recorded from similar systems a multidimensional and multilevel representation of the mission can be abstracted, which can be subsequently converted into a robotic controller. This work, which focuses on the control of a team of robots to play the complex game of football, is divided into three sections: In the first section we investigate the use of spatial structures in team games. Experimental results show that cooperative teams beat groups of individuals when competing for space and that controlling space is important in the game of robot football. In the second section, we generate a multilevel representation of robot football based on spatial structures measured in recorded matches. By differentiating between spatial configurations appearing in desirable and undesirable situations, we can abstract a strategy composed of the more desirable structures. In the third section, five partial strategies are generated, based on the abstracted structures, and a suitable controller is devised. A set of experiments shows the success of the method in reproducing those key structures in a multirobot system. Finally, we compile our methods into a formal architecture for task abstraction and control. The thesis concludes that generating multirobot control algorithms using task abstraction is appropriate for problems which are complex, weakly-defined, multilevel, dynamic, competitive, unpredictable, and which display emergent properties

A Path-Based Procedural Approach for Inferring Playable Game Levels

Video-jogos de hoje, quer consideremos experiências de um jogador, ou ambientes multi-jogador com comunidades de grande dimensão, enfrentam um desafio significante no que concerne o que conseguem oferecer ao jogador. Independentemente do tempo gasto num projecto, o conteúdo que tradicionalmente está disponível para o jogador chega a um fim, quer em quantidade, onde já não restam experiências novas para o jogador, quer em experiências, onde um jogador pode continuar a jogar, com o custo de consumir o mesmo conteúdo de forma repetida, normalmente consistindo nos mesmo níveis, personagens, e mais.A resposta moderna a este problema depende de geração procedimental. Evitando a sobre-utilização de trabalho manual, que pode ter muito custo, tanto em tempo como dinheiro, através de uma esperta utilização de aleatoriedade com inteligente combinação de sistemas e recursos inerentes ao jogo, é possível criar experiências que fornecem ao jogador conteúdo que nunca realmente se repite.No entanto, a geração deste tipo de conteúdo é relativamente complexa e específica a cada jogo e experiência. Doravante, seria inerentemente interessante ter um método simplificado de estabelecer regras de geração procedimental para esse mesmo tipo de conteúdo, e também facilmente gerar esse conteúdo dentro de atributos e restrições bem definidos.Logo, a solução proposta consiste no desenvolvimento desse mesmo método de geração de conteúdo. Com a ajuda dos sensores presentes num telemóvel, pretendemos capturar dados relativos a localização, ao longo de mais dados como a quantidade de luz em determinados locais, ou talvez até som. Depois desenvolveremos uma ferramenta capaz de trabalhar com estes dados e, de acordo com parâmetros fornecidos pelo utilizador, gerar conteúdo jogável que consista sempre numa experiência nova e não-repetida.Finalmente, é necessário estudar cuidadosamente a confiança do conteúdo resultante, questionando possíveis utilizadores e concluindo se estas experiências procedimentais serão de facto fáceis de criar, e disfrutáveis para o jogador.Video games of today, whether we consider single player experiences, or multiplayer environments with massive sprawling communities, face a significant challenge in what they can offer a player. No matter how much time a developer spends on a project, the traditional content that is available to its users eventually reaches an end, either in quantity, where there are no more experiences available to the player, or in regards to experience, where a player can continue playing, at the cost of going through repeated content, usually consisting of the same levels, characters, and more.The modern answer to this problem relies on procedural generation. Avoiding the overuse of manual labor, which can be costly, both time-wise and money-wise, the smart utilization of randomness with the clever matching of in-game assets and systems, developers can create experiences that provide content to the player that never truly repeats itself.However, the generation of this type of content is still relatively complex and specific to each game and experience. Therefore, it would be inherently interesting to have a simplified method of establishing content generation rules for procedural content and also to easily generate that content inside well established attributes and constraints.Therefore, the proposed solution consists of developing the means to that very same method of content generation. With the help of sensors typically present in a mobile phone, we intend to capture location-related data, possibly along with other data such as the amount of light in said location, perhaps even pressure or sound. We shall then develop a tool capable of operating on this data and according to user-provided parameters, generate playable content that is always new and a fresh experience.Finally, we need to carefully study the reliability of the resulting content, surveying possible users and concluding whether these procedural experiences are truly easy to create, and enjoyable for the player

Evolving artificial terrains with automated genetic terrain programing

La industria del videojuego afronta en la actualidad un gran reto: mantener el coste del desarrollo de los proyectos bajo control a medida que estos crecen y se hacen más complejos. La creación de los contenidos de los juegos, que incluye el modelado de personajes, mapas y niveles, texturas, efectos sonoros, etc, representa una parte fundamental del costo final de producción. Por eso, la industria está cada vez más interesada en la utilización de métodos procedurales de generación automática de contenidos. Sin embargo, crear y afinar los métodos procedurales no es una tarea trivial. En esta memoria, se describe un método procedural basado en Programación Genética, que permite la generación automática de terrenos para videojuegos. Los terrenos presentan características estéticas, y no requieren ningún tipo de parametrización para definir su aspecto. Así, el ahorro de tiempo y la reducción de costes en el proceso de producción es notable. Para conseguir los objetivos, se utiliza Programación Genética de Terrenos. La primera implementación de GTP utilizó Evolución Interactiva, en que la presencia del usuario que guía el proceso evolutivo es imprescindible. A pesar de los buenos resultados, el método está limitado por la fatiga del usuario (común en los métodos interactivos). Para resolver esta cuestión se desarrolla un nuevo modelo de GTP en el que el proceso de búsqueda es completamente automático, y dirigido por una función de aptitudo. La función considera accesibilidad de los terrenos y perímetros de los obstáculos. Los resultados obtenidos se incluyeron como parte de un videojuego real.Nowadays video game industry is facing a big challenge: keep costs under control as games become bigger and more complex. Creation of game content, such as character models, maps, levels, textures, sound effects and so on, represent a big slice of total game production cost. Hence, video game industry is increasingly turning to procedural content generation to amplify the cost-effectiveness of video game designers' efforts. However, creating and fine tunning procedural methods for automated content generation is a time consuming task. In this thesis we detail a Genetic Programming based procedural content technique to generate procedural terrains. Those terrains present aesthetic appeal and do not require any parametrization to control its look. Thus, allowing to save time and help reducing production costs. To accomplish these features we devised the Genetic Terrain Programming (GTP) technique. The first implementation of GTP used an Interactive Evolutionary Computation (IEC) approach, were a user guides the evolutionary process. In spite of the good results achieved this way, this approach was limited by user fatigue (common in IEC systems). To address this issue a second version of GTP was developed where the search is automated, being guided by a direct fitness function. That function is composed by two morphological metrics: terrain accessibility and obstacle edge length. The combination of the two metrics allowed us remove the human factor form the evolutionary process and to find a wide range of aesthetic and fit terrains. Procedural terrains produced by GTP are already used in a real video game.Ministerio de Educación y Ciencia (TIN2007-68083-C02-01); (TIN2008-05941); (TIN2011-28627-C04) Junta de Extremadura (GRU-09105); (GR10029) Junta de Andalucía (TIC-6083

VSO: Self-organizing Spatial Publish Subscribe

Abstract-Spatial publish subscribe (SPS) is a basic primitive underlying many real-time, interactive applications such as online games or discrete-time simulations. Supporting SPS on a large-scale, however, requires sufficient resources and proper load distribution among the simulation units. For load distribution, existing mechanisms either use a static partitioning, such that over-provisioning or overloading are bound to occur, or require manual adjustments unsuitable for massive workloads. We describe Voronoi Self-organizing Overlay (VSO) [1], which extends a Voronoi-based Overlay network (VON) to automatically partition and manage a logical space to support SPS. Efficient resource usage thus is possible as only the units necessary to maintain the system are used. Load is also balanced among the resource units so that overloading or overprovisioning can be avoided. We use simulations to verify our design and describe some preliminary results

Voxel-Space Shape Grammars

The field of Procedural Generation is being increasingly used in modern content generation for its ability to significantly decrease the cost and time involved. One such area of Procedural Generation is Shape Grammars, a type of formal grammar that operates on geometric shapes instead of symbols. Conventional shape grammar implementations use mesh representations of shapes, but this has two significant drawbacks. Firstly, mesh representations make Boolean geometry operations on shapes difficult to accomplish. Boolean geometry operations allow us to combine shapes using Boolean operators (and, or, not), producing complex, composite shapes. A second drawback is that sub-, or trans-shape detailing is challenging to achieve. To address these two problems with conventional mesh-based shape grammars, we present a novel extension to shape grammars, in which a voxel representation of the generated shapes is used. We outline a five stage algorithm for using these extensions and discuss a number of optional enhancements and optimizations. The final output of the algorithm is a detailed mesh model, suitable for use in real-time or offline graphics applications. We also test our extension’s performance and range of output with three categories of testing: performance testing, output range testing, and variation testing. The results of the testing with our proof-of-concept implementation show that our unoptimized algorithm is slower than conventional shape grammar implementations, with a running time that is O(N^3) for an N^3 voxel grid. However, there is scope for further optimization to our algorithm, which would significantly reduce running times and memory consumption. We outline and discuss several such avenues for performance enhancement. Additionally, testing reveals that our algorithm is able to successfully produce a broad range of detailed outputs, exhibiting many features that would be very difficult to accomplish using mesh-based shape grammar implementations. This range of 3D models includes fractals, skyscraper buildings, space ships, castles, and more. Further, stochastic rules can be used to produce a variety of models that share a basic archetype, but differ noticeably in their details

Hypernetworks Analysis of RoboCup Interactions

Robotic soccer simulations are controlled environments in which the rich variety of interactions among agents make them good candidates to be studied as complex adaptive systems. The challenge is to create an autonomous team of soccer agents that can adapt and improve its behaviour as it plays other teams. By analogy with chess, the movements of the soccer agents and the ball form ever-changing networks as players in one team form structures that give their team an advantage. For example, the Defender’s Dilemma involves relationships between an attacker with the ball, a team-mate and a defender. The defender must choose between tackling the player with the ball, or taking a position to intercept a pass to the other attacker. Since these structures involve more that two interacting entities it is necessary to go beyond networks to multidimensional hypernetworks. In this context, this thesis investigates (i) is it possible to identify patterns of play, that lead a team to obtain an advantage ?, (ii) is it possible to forecast with a good degree of accuracy if a certain game action or sequence of game actions is going to be successful, before it has been completed ?, and (iii) is it possible to make behavioural patterns emerge in the game without specifying the behavioural rules in detail ? To investigate these research questions we devised two methods to analyse the interactions between robotic players, one based on traditional programming and one based on Deep Learning. The first method identified thousands of Defender’s Dilemma configurations from RoboCup 2D simulator games and found a statistically significant association between winning and the creation of the defender’s dilemma by the attackers of the winning team. The second method showed that a feedforward Artificial Neural Network trained on thousands of games can take as input the current game configuration and forecast to a high degree of accuracy if the current action will end up in a goal or not. Finally, we designed our own fast and simple robotic soccer simulator for investigating Reinforcement Learning. This showed that Reinforcement Learning using Proximal Policy Optimization could train two agents in the task of scoring a goal, using only basic actions without using pre-built hand-programmed skills. These experiments provide evidence that it is possible: to identify advantageous patterns of play; to forecast if an action or sequence of actions will be successful; and to make behavioural patterns emerge in the game without specifying the behavioural rules in detail