A comprehensive study on pathfinding techniques for robotics and video games

This survey provides an overview of popular pathfinding algorithms and techniques based on graph generation problems. We focus on recent developments and improvements in existing techniques and examine their impact on robotics and the video games industry. We have categorized pathfinding algorithms based on a 2D/3D environment search. The aim of this paper is to provide researchers with a thorough background on the progress made in the last 10 years in this field, summarize the principal techniques, and describe their results. We also give our expectations for future trends in this field and discuss the possibility of using pathfinding techniques in more extensive areas

Rectangle expansion A∗ pathfinding for grid maps

AbstractSearch speed, quality of resulting paths and the cost of pre-processing are the principle evaluation metrics of a pathfinding algorithm. In this paper, a new algorithm for grid-based maps, rectangle expansion A∗ (REA∗), is presented that improves the performance of A∗ significantly. REA∗ explores maps in units of unblocked rectangles. All unnecessary points inside the rectangles are pruned and boundaries of the rectangles (instead of individual points within those boundaries) are used as search nodes. This makes the algorithm plot fewer points and have a much shorter open list than A∗. REA∗ returns jump and grid-optimal path points, but since the line of sight between jump points is protected by the unblocked rectangles, the resulting path of REA∗ is usually better than grid-optimal. The algorithm is entirely online and requires no offline pre-processing. Experimental results for typical benchmark problem sets show that REA∗ can speed up a highly optimized A∗ by an order of magnitude and more while preserving completeness and optimality. This new algorithm is competitive with other highly successful variants of A∗

Review Algoritma C-Theta* dan Prospek Implementasinya di Masa Depan

Perencanaan jalan digunakan untuk menentukan jalan yang akan dilalui oleh agen agar dapat mencapai tujuannya. Penggunaan perencanaan jalan tidak hanya diterapkan pada game melainkan juga diterapkan pada robot dan mesin lainnya yang memiliki kemampuan untuk bergerak. C-Theta* merupakan algoritma perencanaan jalan baru dengan kecepatan perencanaan dan hasil perencanaan yang lebih baik dibandingkan dengan pendahulunya, algoritma A* dan Theta*. Tentunya sebagai algoritma yang baru C-Theta* belum memiliki penelitian lebih lanjut mengenai prospek implementasinya di masa depan, sehingga para peneliti tidak dapat mengetahui apakah algoritma ini dapat diimplementasikan pada penelitiannya. Demi mengembangkan algoritma perencanaan jalan di berbagai bidang maka perlu dilakukan penelitian lebih lanjut untuk mencari tahu prospek implementasi dari algoritma C-Theta* di masa depan. Penelitian ini bertujuan untuk memberi review mengenai C-Theta* dengan melakukan komparasi C-Theta* dengan algoritma perencanaan jalan lainnya dan menganalisa kasus pada penelitian lain untuk mencari tahu kemungkinan bagi algoritma ini untuk dapat diimplementasikan atau tidak

Identification of metabolic pathways using pathfinding approaches: A systematic review

Metabolic pathways have become increasingly available for variousmicroorganisms. Such pathways have spurred the development of a wide array of computational tools, in particular, mathematical pathfinding approaches. This article can facilitate the understanding of computational analysis ofmetabolic pathways in genomics. Moreover, stoichiometric and pathfinding approaches inmetabolic pathway analysis are discussed. Threemajor types of studies are elaborated: stoichiometric identification models, pathway-based graph analysis and pathfinding approaches in cellular metabolism. Furthermore, evaluation of the outcomes of the pathways withmathematical benchmarkingmetrics is provided. This review would lead to better comprehension ofmetabolismbehaviors in living cells, in terms of computed pathfinding approaches. © The Author 2016

Toward human-like pathfinding with hierarchical approaches and the GPS of the brain theory

Pathfinding for autonomous agents and robots has been traditionally driven by finding optimal paths. Where typically optimality means finding the shortest path between two points in a given environment. However, optimality may not always be strictly necessary. For example, in the case of video games, often computing the paths for non-player characters (NPC) must be done under strict time constraints to guarantee real time simulation. In those cases, performance is more important than finding the shortest path, specially because often a sub-optimal path can be just as convincing from the point of view of the player. When simulating virtual humanoids, pathfinding has also been used with the same goal: finding the shortest path. However, humans very rarely follow precise shortest paths, and thus there are other aspects of human decision making and path planning strategies that should be incorporated in current simulation models. In this thesis we first focus on improving performance optimallity to handle as many virtual agents as possible, and then introduce neuroscience research to propose pathfinding algorithms that attempt to mimic humans in a more realistic manner.In the case of simulating NPCs for video games, one of the main challenges is to compute paths as efficiently as possible for groups of agents. As both the size of the environments and the number of autonomous agents increase, it becomes harder to obtain results in real time under the constraints of memory and computing resources. For this purpose we explored hierarchical approaches for two reasons: (1) they have shown important performance improvements for regular grids and other abstract problems, and (2) humans tend to plan trajectories also following an topbottom abstraction, focusing first on high level location and then refining the path as they move between those high level locations. Therefore, we believe that hierarchical approaches combine the best of our two goals: improving performance for multi-agent pathfinding and achieving more human-like pathfinding. Hierarchical approaches, such as HNA* (Hierarchical A* for Navigation Meshes) can compute paths more efficiently, although only for certain configurations of the hierarchy. For other configurations, the method suffers from a bottleneck in the step that connects the Start and Goal positions with the hierarchy. This bottleneck can drop performance drastically.In this thesis we present different approaches to solve the HNA* bottleneck and thus obtain a performance boost for all hierarchical configurations. The first method relies on further memory storage, and the second one uses parallelism on the GPU. Our comparative evaluation shows that both approaches offer speed-ups as high as 9x faster than A*, and show no limitations based on hierarchical configuration. Then we further exploit the potential of CUDA parallelism, to extend our implementation to HNA* for multi-agent path finding. Our method can now compute paths for over 500K agents simultaneously in real-time, with speed-ups above 15x faster than a parallel multi-agent implementation using A*. We then focus on studying neurosience research to learn about the way that humans build mental maps, in order to propose novel algorithms that take those finding into account when simulating virtual humans. We propose a novel algorithm for path finding that is inspired by neuroscience research on how the brain learns and builds cognitive maps. Our method represents the space as a hexagonal grid, based on the GPS of the brain theory, and fires memory cells as counters. Our path finder then combines a method for exploring unknown environments while building such a cognitive map, with an A* search using a modified heuristic that takes into account the GPS of the brain cognitive map.El problema de Pathfinding para agentes autónomos o robots, ha consistido tradicionalmente en encontrar un camino óptimo, donde por óptimo se entiende el camino de distancia mínima entre dos posiciones de un entorno. Sin embargo, en ocasiones puede que no sea estrictamente necesario encontrar una solución óptima. Para ofrecer la simulación de multitudes de agentes autónomos moviéndose en tiempo real, es necesario calcular sus trayectorias bajo condiciones estrictas de tiempo de computación, pero no es fundamental que las soluciones sean las de distancia mínima ya que, con frecuencia, el observador no apreciará la diferencia entre un camino óptimo y un sub-óptimo. Por tanto, suele ser suficiente con que la solución encontrada sea visualmente creíble para el observado. Cuando se simulan humanoides virtuales en aplicaciones de realidad virtual que requieren avatares que simulen el comportamiento de los humanos, se tiende a emplear los mismos algoritmos que en video juegos, con el objetivo de encontrar caminos de distancia mínima. Pero si realmente queremos que los avatares imiten el comportamiento humano, tenemos que tener en cuenta que, en el mundo real, los humanos rara vez seguimos precisamente el camino más corto, y por tanto se deben considerar otros aspectos que influyen en la toma de decisiones de los humanos y la selección de rutas en el mundo real. En esta tesis nos centraremos primero en mejorar el rendimiento de la búsqueda de caminos para poder simular grandes números de humanoides virtuales autónomos, y a continuación introduciremos conceptos de investigación con mamíferos en neurociencia, para proponer soluciones al problema de pathfinding que intenten imitar con mayor realismo, el modo en el que los humanos navegan el entorno que les rodea. A medida que aumentan tanto el tamaño de los entornos virtuales como el número de agentes autónomos, resulta más difícil obtener soluciones en tiempo real, debido a las limitaciones de memoria y recursos informáticos. Para resolver este problema, en esta tesis exploramos enfoques jerárquicos porque consideramos que combinan dos objetivos fundamentales: mejorar el rendimiento en la búsqueda de caminos para multitudes de agentes y lograr una búsqueda de caminos similar a la de los humanos. El primer método presentado en esta tesis se basa en mejorar el rendimiento del algoritmo HNA* (Hierarchical A* for Navigation Meshes) incrementando almacenamiento de datos en memoria, y el segundo utiliza el paralelismo para mejorar drásticamente el rendimiento. La evaluación cuantitativa realizada en esta tesis, muestra que ambos enfoques ofrecen aceleraciones que pueden llegar a ser hasta 9 veces más rápidas que el algoritmo A* y no presentan limitaciones debidas a la configuración jerárquica. A continuación, aprovechamos aún más el potencial del paralelismo ofrecido por CUDA para extender nuestra implementación de HNA* a sistemas multi-agentes. Nuestro método permite calcular caminos simultáneamente y en tiempo real para más de 500.000 agentes, con una aceleración superior a 15 veces la obtenida por una implementación paralela del algoritmo A*. Por último, en esta tesis nos hemos centrado en estudiar los últimos avances realizados en el ámbito de la neurociencia, para comprender la manera en la que los humanos construyen mapas mentales y poder así proponer nuevos algoritmos que imiten de forma más real el modo en el que navegamos los humanos. Nuestro método representa el espacio como una red hexagonal, basada en la distribución de ¿place cells¿ existente en el cerebro, e imita las activaciones neuronales como contadores en dichas celdas. Nuestro buscador de rutas combina un método para explorar entornos desconocidos mientras construye un mapa cognitivo hexagonal, utilizando una búsqueda A* con una nueva heurística adaptada al mapa cognitivo del cerebro y sus contadores

Group navigation in RTS games using flow networks over flow field regions

This thesis explores the challenges of implementing effective navigation for groups of units in real-time strategy computer games, specifically focusing on the movement of large numbers of homogeneous units across a two-dimensional grid-based map. The thesis presents a pathfinding algorithm that could be used in RTS games. The algorithm enables the units to utilize multiple paths effectively by modeling the unit navigation as a flow network problem. The units use precomputed flow fields during the navigation. This allows for faster pathfinding times by offloading part of the computation to the preprocessing. The algorithm's performance is evaluated against a baseline solution using the A* algorithm and other existing solutions. Comparative analysis will be conducted utilizing maps from the Moving AI 2D Pathfinding Benchmark dataset to assess the efficacy of the proposed solution. 1Tato diplomová práce zkoumá problém implementace efektivní navigace pro skupiny jednotek v real-time strategických počítačových hrách, konkrétně na pohych velkého množství stejnorodých jednotek na dvou-dimenzionální mapě. Práce navrhuje navigační algoritmus, který by bylo možné použít v RTS hrách. Algo- ritmus umožňuje jednotkám efektivně využit alternativní cesty díky modelování navigace jednotek pomocí toků v síti. Jednotky během své navigace používají předpočítaná vek- torová pole. To umožňuje dosažení rychlejšího nalezení cesty díky přesunutí části výpočtu do fáze preprocessingu. Efektivita algoritmu je porovnána proti základním řešenim využívajícím A*, nebo a jiné běžné navigační algoritmy. K posouzení účinnosti navrhovaného algorimu bude prove- dena srovnávací analýza s využitím map z datového souboru Moving AI 2D Pathfinding Benchmark. 1Department of Software and Computer Science EducationKatedra softwaru a výuky informatikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Semi-autonomous robotic wheelchair controlled with low throughput human- machine interfaces

For a wide range of people with limited upper- and lower-body mobility, interaction with robots remains a challenging problem. Due to various health conditions, they are often unable to use standard joystick interface, most of wheelchairs are equipped with. To accommodate this audience, a number of alternative human-machine interfaces have been designed, such as single switch, sip-and-puff, brain-computer interfaces. They are known as low throughput interfaces referring to the amount of information that an operator can pass into the machine. Using them to control a wheelchair poses a number of challenges. This thesis makes several contributions towards the design of robotic wheelchairs controlled via low throughput human-machine interfaces: (1) To improve wheelchair motion control, an adaptive controller with online parameter estimation is developed for a differentially driven wheelchair. (2) Steering control scheme is designed that provides a unified framework integrating different types of low throughput human-machine interfaces with an obstacle avoidance mechanism. (3) A novel approach to the design of control systems with low throughput human-machine interfaces has been proposed. Based on the approach, position control scheme for a holonomic robot that aims to probabilistically minimize time to destination is developed and tested in simulation. The scheme is adopted for a real differentially driven wheelchair. In contrast to other methods, the proposed scheme allows to use prior information about the user habits, but does not restrict navigation to a set of pre-defined points, and parallelizes the inference and motion reducing the navigation time. (4) To enable the real time operation of the position control, a high-performance algorithm for single-source any-angle path planning on a grid has been developed. By abandoning the graph model and introducing discrete geometric primitives to represent the propagating wave front, we were able to design a planning algorithm that uses only integer addition and bit shifting. Experiments revealed a significant performance advantage. Several modifications, including optimal and multithreaded implementations, are also presented

Video game pathfinding and improvements to discrete search on grid-based maps

The most basic requirement for any computer controlled game agent in a video game is to be able to successfully navigate the game environment. Pathfinding is an essential component of any agent navigation system. Pathfinding is, at the simplest level, a search technique for finding a route between two points in an environment. The real-time multi-agent nature of video games places extremely tight constraints on the pathfinding problem. This study aims to provide the first complete review of the current state of video game pathfinding both in regards to the graph search algorithms employed as well as the implications of pathfinding within dynamic game environments. Furthermore this thesis presents novel work in the form of a domain specific search algorithm for use on grid-based game maps: the spatial grid A* algorithm which is shown to offer significant improvements over A* within the intended domain. CopyrightDissertation (MSc)--University of Pretoria, 2011.Computer Scienceunrestricte

Theoretical Computational Models for the Cognitive Map

In den letzten Jahrzehnten hat die Forschung nach der Frage, wie Raum im Gehirn repräsentiert wird, ein weit verzweigtes Netzwerk von spezialisierten Zellen aufgedeckt. Es ist nun klar, dass Räumlichkeit auf irgendeine Art repräsentiert sein muss, aber die genaue Umsetzung wird nach wie vor debattiert. Folgerichtig liegt das übergeordnete Ziel meiner Dissertation darin, das Verständnis von der neuronalen Repräsentation, der Kognitiven Karte, mithilfe von theoretischer Computermodellierung (im Gegensatz zu datengetriebener Modellierung) zu erweitern. Die Arbeit setzt sich aus vier Publikationen zusammen, die das Problem aus verschiedenen, aber miteinander kompatiblen Richtungen angehen: In den ersten beiden Publikationen geht es um zielgerichtete Navigation durch topologische Graphen, in denen die erkundete Umgebung als Netzwerk aus loka len Positionen und sie verbindenden Handlungen dargestellt wird. Im Gegensatz zu Koordinaten-basierten metrischen Karten sind Graphenmodelle weniger gebunden und haben verschiedene Vorteile wie z.B. Algorithmen, die garantiert optimale Pfade finden. Im ersten Modell sind Orte durch Populationen von einfachen Bildfeatures im Graphen gespeichert. Für die Navigation werden dann mehrere Pfade gleichzeitig zwischen Start- und Zielpopulationen berechnet und die schlussendliche Route folgt dem Durchschnitt der Pfade. Diese Methode macht die Wegsuche robuster und umgeht das Problem, Orte entlang der Route wiedererkennen zu müssen. In der zweiten Publikation wird ein hierarchisches Graphenmodell vorgeschlagen, bei dem die Umgebung in mehrere Regionen unterteilt ist. Das Regionenwissen ist ebenfalls als übergeordnete Knoten im Graphen gespeichert. Diese Struktur führt bei der Wegsuche dazu, dass die berechneten Routen verzerrt sind, was mit dem Verhalten von menschlichen Probanden in Navigationsstudien übereinstimmt. In der dritten Publikation geht es auch um Regionen, der Fokus liegt aber auf der konkreten biologischen Umsetzung in Form von Place Cell und Grid Cell-Aktivität. Im Gegensatz zu einzigartigen Ortsknoten im Graphen zeigen Place Cells multiple Feuerfelder in verschiedenen Regionen oder Kontexten. Dieses Phänomen wird als Remapping bezeichnet und könnte der Mechanismus hinter Regionenwissen sein. Wir modellieren das Phänomen mithilfe eines Attraktor-Netzwerks aus Place- und Grid Cells: Immer, wenn sich der virtuelle Agent des Modells von einer Region in eine andere bewegt, verändert sich der Kontext und die Zellaktivität springt zu einem anderen Attraktor, was zu einem Remapping führt. Das Modell kann die Zellaktivität von Tieren in mehreren Experimentalumgebungen replizieren und ist daher eine plausible Erklärung für die Vorgänge im biologischen Gehirn. In der vierten Publikation geht es um den Vergleich von Graphen- und Kartenmodellen als fundamentale Struktur der kognitiven Karte. Im Speziellen geht es bei dieser Debatte um die Unterscheidung zwischen nicht-metrischen Graphen und metrischen euklidischen Karten; euklidische Karten sind zwar mächtiger als die Alternative, aber menschliche Probanden neigen dazu, Fehler zu machen, die stark von einer metrischen Vorhersage abweichen. Deshalb wird häufig argumentiert, dass nicht-metrische Modelle das Verhalten besser erklären können. Wir schlagen eine alternative metrische Erklärung für die nichtmetrischen Graphen vor, indem wir die Graphen im metrischen Raum einbetten. Die Methode wird in einer bestimmten nicht-euklidischen Beispielumgebung gezeigt, in der sie Versuchspersonenverhalten genauso gut vorhersagen kann, wie ein nichtmetrischer Graph. Wir argumentieren daher, dass unser Modell ein besseres Modell für Raumrepräsentation sein könnte. Zusätzlich zu den Einzelergebnissen diskutiere ich außerdem die Gemeinsamkeiten der Modelle und wie sie in den derzeitigen Stand der Forschung zur kognitiven Karte passen. Darüber hinaus erörtere ich, wie die Ergebnisse zu komplexeren Modellen vereint werden könnten, um unser Bild der Raumkognition zu erweitern.Decades of research into the neural representation of physical space have uncovered a complex and distributed network of specialized cells in the mammalian brain. It is now clear that space is represented in some form, but the realization remains debated. Accordingly, the overall aim of my thesis is to further the understanding of the neural representation of space, the cognitive map, with the aid of theoretical computational modeling (as opposed to data-driven modeling). It consists of four separate publications which approach the problem from different but complementing perspectives: The first two publications consider goal-directed navigation with topological graph models, which encode the environment as a state-action graph of local positions connected by simple movement instructions. Graph models are often less constrained than coordinate-based metric maps and offer a variety of computational advantages; for example, graph search algorithms may be used to derive optimal routes between arbitrary positions. In the first model, places are encoded by population codes of low-level image features. For goal-directed navigation, a set of simultaneous paths is obtained between the start and goal populations and the final trajectory follows the population average. This makes route following more robust and circumvents problems related to place recognition. The second model proposes a hierarchical place graph which subdivides the known environment into well-defined regions. The region knowledge is included in the graph as superordinate nodes. During wayfinding, these nodes distort the resulting paths in a way that matches region-related biases observed in human navigation experiments. The third publication also considers region coding but focuses on more concrete biological implementation in the form of place cell and grid cell activity. As opposed to unique nodes in a graph, place cells may express multiple firing fields in different contexts or regions. This phenomenon is known as “remapping” and may be fundamental to the encoding region knowledge. The dynamics are modeled in a joint attractor neural network of place and grid cells: Whenever a virtual agent moves into another region, the context changes and the model remaps the cell activity to an associated pattern from memory. The model is able to replicate experimental findings in a series of mazes and may therefore be an explanation for the observed activity in the biological brain. The fourth publication again returns to graph models, joining the debate on the fundamental structure of the cognitive map: The internal representation of space has often been argued to either take the form of a non-metric topological graph or a Euclidean metric map in which places are assigned specific coordinates. While the Euclidean map is more powerful, human navigation in experiments often strongly deviates from a (correct) metric prediction, which has been taken as an argument for the non-metric alternative. However, it may also be possible to find an alternative metric explanation to the non-metric graphs by embedding the latter into metric space. The method is shown with a specific non-Euclidean example environment where it can explain subject behavior equally well to the purely non-metric graph, and it is argued that it is therefore a better model for spatial knowledge. Beyond the individual results, the thesis discusses the commonalities of the models and how they compare to current research on the cognitive map. I also consider how the findings may be combined into more complex models to further the understanding of the cognitive neuroscience of space