I/O-optimal algorithms on grid graphs

Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M = Omega(B^2): computation of shortest paths with non-negative edge weights from a single source, breadth-first traversal, computation of a minimum spanning tree, topological sorting, time-forward processing (if the input is a plane graph), and an Euler tour (if the input graph is a tree). The minimum-spanning tree algorithm is cache-oblivious. The best previously published algorithms for these problems need Theta(sort(n)) I/Os. Estimates of the actual I/O volume show that the new algorithms may often be very efficient in practice.Comment: 12 pages' extended abstract plus 12 pages' appendix with details, proofs and calculations. Has not been published in and is currently not under review of any conference or journa

Hierarchical path-finding for Navigation Meshes (HNA*)

Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft

Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

Automated generation of geometrically-precise and semantically-informed virtual geographic environnements populated with spatially-reasoning agents

La Géo-Simulation Multi-Agent (GSMA) est un paradigme de modélisation et de simulation de phénomènes dynamiques dans une variété de domaines d'applications tels que le domaine du transport, le domaine des télécommunications, le domaine environnemental, etc. La GSMA est utilisée pour étudier et analyser des phénomènes qui mettent en jeu un grand nombre d'acteurs simulés (implémentés par des agents) qui évoluent et interagissent avec une représentation explicite de l'espace qu'on appelle Environnement Géographique Virtuel (EGV). Afin de pouvoir interagir avec son environnement géographique qui peut être dynamique, complexe et étendu (à grande échelle), un agent doit d'abord disposer d'une représentation détaillée de ce dernier. Les EGV classiques se limitent généralement à une représentation géométrique du monde réel laissant de côté les informations topologiques et sémantiques qui le caractérisent. Ceci a pour conséquence d'une part de produire des simulations multi-agents non plausibles, et, d'autre part, de réduire les capacités de raisonnement spatial des agents situés. La planification de chemin est un exemple typique de raisonnement spatial dont un agent pourrait avoir besoin dans une GSMA. Les approches classiques de planification de chemin se limitent à calculer un chemin qui lie deux positions situées dans l'espace et qui soit sans obstacle. Ces approches ne prennent pas en compte les caractéristiques de l'environnement (topologiques et sémantiques), ni celles des agents (types et capacités). Les agents situés ne possèdent donc pas de moyens leur permettant d'acquérir les connaissances nécessaires sur l'environnement virtuel pour pouvoir prendre une décision spatiale informée. Pour répondre à ces limites, nous proposons une nouvelle approche pour générer automatiquement des Environnements Géographiques Virtuels Informés (EGVI) en utilisant les données fournies par les Systèmes d'Information Géographique (SIG) enrichies par des informations sémantiques pour produire des GSMA précises et plus réalistes. De plus, nous présentons un algorithme de planification hiérarchique de chemin qui tire avantage de la description enrichie et optimisée de l'EGVI pour fournir aux agents un chemin qui tient compte à la fois des caractéristiques de leur environnement virtuel et de leurs types et capacités. Finalement, nous proposons une approche pour la gestion des connaissances sur l'environnement virtuel qui vise à supporter la prise de décision informée et le raisonnement spatial des agents situés

Subregion graph: A path planning acceleration structure for characters with various motion types in very large environments

Modern computer graphics applications commonly feature very large virtual environments and diverse characters which perform different kinds of motions. To accelerate path planning in such a scenario, we propose the subregion graph data structure. It consists of subregions, which are clusters of locally connected waypoints inside a region, as well as subregion connectivities. We also present a fast algorithm to automatically generate a subregion graph from an enhanced waypoint graph map representation, which also supports various motion types and can be created from large virtual environments. Nevertheless, a subregion graph can be generated from any graphbased map representation. Our experiments show that a subregion graph is very compact relative to the input waypoint graph. By firstly planning a subregion path, and then limiting waypoint-level planning to this subregion path, over 8 times average speedup can be achieved, while average length ratios remain as low as 102.5%

Transport on river networks: A dynamical approach

This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network transport is treated as a particular case of nearest-neighbor hierarchical aggregation with respect to the metric induced by the branching structure of the river network. We describe the static geometric structure of a drainage network by a tree, referred to as the static tree, and introduce an associated dynamic tree that describes the transport along the static tree. It is well known that the static branching structure of river networks can be described by self-similar trees (SSTs); we demonstrate that the corresponding dynamic trees are also self-similar. We report an unexpected phase transition in the dynamics of three river networks, one from California and two from Italy, demonstrate the universal features of this transition, and seek to interpret it in hydrological terms.Comment: 38 pages, 15 figure

System of Terrain Analysis, Energy Estimation and Path Planning for Planetary Exploration by Robot Teams

NASA’s long term plans involve a return to manned moon missions, and eventually sending humans to mars. The focus of this project is the use of autonomous mobile robotics to enhance these endeavors. This research details the creation of a system of terrain classification, energy of traversal estimation and low cost path planning for teams of inexpensive and potentially expendable robots. The first stage of this project was the creation of a model which estimates the energy requirements of the traversal of varying terrain types for a six wheel rocker-bogie rover. The wheel/soil interaction model uses Shibly’s modified Bekker equations and incorporates a new simplified rocker-bogie model for estimating wheel loads. In all but a single trial the relative energy requirements for each soil type were correctly predicted by the model. A path planner for complete coverage intended to minimize energy consumption was designed and tested. It accepts as input terrain maps detailing the energy consumption required to move to each adjacent location. Exploration is performed via a cost function which determines the robot’s next move. This system was successfully tested for multiple robots by means of a shared exploration map. At peak efficiency, the energy consumed by our path planner was only 56% that used by the best case back and forth coverage pattern. After performing a sensitivity analysis of Shibly’s equations to determine which soil parameters most affected energy consumption, a neural network terrain classifier was designed and tested. The terrain classifier defines all traversable terrain as one of three soil types and then assigns an assumed set of soil parameters. The classifier performed well over all, but had some difficulty distinguishing large rocks from sand. This work presents a system which successfully classifies terrain imagery into one of three soil types, assesses the energy requirements of terrain traversal for these soil types and plans efficient paths of complete coverage for the imaged area. While there are further efforts that can be made in all areas, the work achieves its stated goals