On the hardness of unlabeled multi-robot motion planning

In unlabeled multi-robot motion planning several interchangeable robots operate in a common workspace. The goal is to move the robots to a set of target positions such that each position will be occupied by some robot. In this paper, we study this problem for the specific case of unit-square robots moving amidst polygonal obstacles and show that it is PSPACE-hard. We also consider three additional variants of this problem and show that they are all PSPACE-hard as well. To the best of our knowledge, this is the first hardness proof for the unlabeled case. Furthermore, our proofs can be used to show that the labeled variant (where each robot is assigned with a specific target position), again, for unit-square robots, is PSPACE-hard as well, which sets another precedence, as previous hardness results require the robots to be of different shapes

Gourds: A Sliding-Block Puzzle with Turning

We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.Comment: 15 pages + 3 pages appendix, including 18 figure

Resolución del juego Sokoban con técnicas de búsqueda

La búsqueda es una rama principal de la Inteligencia Artificial (IA) que se encarga de encontrar solucion a los problemas mediante su representacion en diferentes estados. Los juegos siempre han servido como campo de pruebas de estas tecnicas. En esta ocasion se aplica la búsqueda de un solo agente para resolver los niveles del juego Sokoban de forma optima. Esta tarea es realmente complicada por la gran cantidad de movimientos posibles en cada una de las situaciones del jugador. Además, las soluciones necesitan una larga sucesion de movimientos para encontrar la meta. A estas dificultades se le suma la posibilidad de alcanzar posiciones que impiden que el problema se pueda resolver, lo que lo complica aún más. Todo esto provoca que sea prácticamente imposible resolver algún nivel con búsqueda. Para abordar este problema se realiza un estudio exhaustivo de los objetivos que se quieren alcanzar y de las investigaciones anteriores. Esto nos ayuda a establecer todas las funcionalidades necesarias, a plantear las decisiones de diseño adecuadas y a implementar diferentes alternativas para encontrar el mejor agente. Para solucionar este problema se diseñan diferentes tecnicas, como localizar posiciones que impiden alcanzar la meta o eliminar los estados que se repitan a lo largo de la búsqueda, que ayudan a reducir la dimension del problema. A continuacion, se implementan diferentes algoritmos de búsqueda y las correspondientes heurísticas con el objetivo de alcanzar la solucion optima de cada uno de los niveles. Además de resolver los problemas durante este proyecto se realiza una comparativa entre los diferentes experimentos realizados con la finalidad de analizar la importancia de las heurísticas. Una vez obtenidos todos los resultados se elige la mejor configuracion encontrada y se analizan las ventajas e inconvenientes que se encuentran, con el objetivo de mejorar en futuros trabajos.Search is a central topic in Artificial Intelligence that is responsible for solving problems through their representation in different states. Games have always been used as a test of these techniques. In this dissertation, search single agent is applied to optimally solve Sokoban game levels. This is a very complicated task due to the large number of possible moves the player has at every state. In addition, solutions are composed of long sequences of moves to find goal These difficulties are compounded by the possibility of reaching positions that prevent the problem from being solved, which further complicates this problem. All this makes it virtually impossible to solve some of the levels. To approach this problem, it is performed a comprehensive study of the objectives to be achieved as well as a study of other previous research. This helps us establish all necessary functionalities, to propose appropriate design decisions and to implement dfferent alternatives to find the best agent. Initially, different techniques are designed to solve this problem, such as locating reachable positions that prevent from achieving the goal or eliminating repeated states along the search, which helps reduce the dimension of the problem. Then, different algorithms are implemented with the corresponding search heuristics in order to reach the optimal solution in each level. In addition to solving the problems, in this project, different experiments are compared in order to analyze the importance of the heuristics. Once all results have been obtained, the best model is chosen and the advantages and disadvantages are discussed to provide with future work lines.Ingeniería Informátic

Enhancing automatic level generation for platform videogames

This dissertation addresses the challenge of improving automatic level generation processes for plat-form videogames. As Procedural Content Generation (PCG) techniques evolved from the creation of simple elements to the construction of complete levels and scenarios, the principles behind the generation algorithms became more ambitious and complex, representing features that beforehand were only possible with human design. PCG goes beyond the search for valid geometries that can be used as levels, where multiple challenges are represented in an adequate way. It is also a search for user-centred design content and the creativity sparks of humanly created content. In order to improve the creativity capabilities of such generation algorithms, we conducted part of our research directed to the creation of new techniques using more ambitious design patterns. For this purpose, we have implemented two overall structure generation algorithms and created an addi-tional adaptation algorithm. The later can transform simple branched paths into more compelling game challenges by adding items and other elements in specific places, such as gates and levers for their activation. Such approach is suitable to avoid excessive level linearity and to represent certain design patterns with additional content richness. Moreover, content adaptation was transposed from general design domain to user-centred principles. In this particular case, we analysed success and failure patterns in action videogames and proposed a set of metrics to estimate difficulty, taking into account that each user has a different perception of that concept. This type of information serves the generation algorithms to make them more directed to the creation of personalised experiences. Furthermore, the conducted research also aimed to the integration of different techniques into a common ground. For this purpose, we have developed a general framework to represent content of platform videogames, compatible with several titles within the genre. Our algorithms run over this framework, whereby they are generic and game independent. We defined a modular architecture for the generation process, using this framework to normalise the content that is shared by multiple modules. A level editor tool was also created, which allows human level design and the testing of automatic generation algorithms. An adapted version of the editor was implemented for the semi-automatic creation of levels, in which the designer may simply define the type of content that he/she desires, in the form of quests and missions, and the system creates a corresponding level structure. This materialises our idea of bridging human high-level design patterns with lower level automated generation algorithms. Finally, we integrated the different contributions into a game prototype. This implementation allowed testing the different proposed approaches altogether, reinforcing the validity of the proposed archi-tecture and framework. It also allowed performing a more complete gameplay data retrieval in order to strengthen and validate the proposed metrics regarding difficulty perceptions

Mobile Robots Navigation

Mobile robots navigation includes different interrelated activities: (i) perception, as obtaining and interpreting sensory information; (ii) exploration, as the strategy that guides the robot to select the next direction to go; (iii) mapping, involving the construction of a spatial representation by using the sensory information perceived; (iv) localization, as the strategy to estimate the robot position within the spatial map; (v) path planning, as the strategy to find a path towards a goal location being optimal or not; and (vi) path execution, where motor actions are determined and adapted to environmental changes. The book addresses those activities by integrating results from the research work of several authors all over the world. Research cases are documented in 32 chapters organized within 7 categories next described

Rolling block mazes are PSPACE-complete

In a rolling block maze, one or more blocks lie on a rectangular board with square cells. In most mazes, the blocks have size k × m × n where k, m, n are integers that determine the size of the block in terms of units of the size of the board cells. The task of a rolling block maze is to roll a particular block from a starting to an ending placement. A block is rolled by tipping it over one of its edges. Some of the squares of the board are marked as forbidden to roll on. We show that solving rolling block mazes is PSPACE-complete